W. Lang, Apr 30 2010 A176726/A176727 rationals, a-sequence for the Sheffer triangle A060081. A general exposition of a- and z-sequences for Sheffer triangles and the recurrences they imply for such triangles is given in a W. Lang link in A006232. Rationals generated exponentially by a(x)= x/ln(sqrt((1+x)/(1-x))), called a-sequence for the Sheffer triangle A060081 (1/cosh(x),tanh(x)), for n=0..60: [1, 0, -2/3, 0, -32/15, 0, -704/21, 0, -54784/45, 0, -2610176/33, 0, -10976325632/1365, 0, -52971659264/45, 0, -179326416191488/765, 0, -24309257264168960/399, 0, -69389116291423404032/3465, 0, -8404514249426618810368/1035, 0, -81520321871322828385550336/20475, 0, -438807077783516207378333696/189, 0, -690781531822985516802849636352/435, 0, -9015729901041514139206131264782336/7161, 0, -67463316677926730703077749205680259072/58905, 0, -373229039147406817559513102209488257024/315, 0, -1327331369171479446151106148111071922228297728/959595, 0, -211730913558316674652905303604838498893299712/117, 0, -53518340033122735502700307228578213730164800487424/20295, 0, -634176988327088786835712165844223781051929509289263104/148995, 0, -822885923194498710357298221074572955152536537979317911552/108675, 0, -218812888854550994131922548781963537024016844836662771974144/14805, 0, -76804196927422755549229113088969765542308628409059466945941733376/2436525, 0, -4803650995121609298573378904095709129475287642206414393978696761344/65637, 0, -14507421558005072130327637953973574293485062693888983142604638397661184/78705, 0, -11016928188325987419091310207037801643816796072586451381916577107441352704/21945, 0, -36552549980897045514699595181548502665391559659618587536128150553039982297088/24795, 0, -2471616932593483550143673642498647085928426759655827713990033546183972457807872/531, 0]. Numerators A176726(n), n=0..60: [1, 0, -2, 0, -32, 0, -704, 0, -54784, 0, -2610176, 0, -10976325632, 0, -52971659264, 0, -179326416191488, 0, -24309257264168960, 0, -69389116291423404032, 0, -8404514249426618810368, 0, -81520321871322828385550336, 0, -438807077783516207378333696, 0, -690781531822985516802849636352, 0, -9015729901041514139206131264782336, 0, -67463316677926730703077749205680259072, 0, -373229039147406817559513102209488257024, 0, -1327331369171479446151106148111071922228297728, 0, -211730913558316674652905303604838498893299712, 0, -53518340033122735502700307228578213730164800487424, 0, -634176988327088786835712165844223781051929509289263104, 0, -822885923194498710357298221074572955152536537979317911552, 0, -218812888854550994131922548781963537024016844836662771974144, 0, -76804196927422755549229113088969765542308628409059466945941733376, 0, -4803650995121609298573378904095709129475287642206414393978696761344, 0, -14507421558005072130327637953973574293485062693888983142604638397661184, 0, -11016928188325987419091310207037801643816796072586451381916577107441352704, 0, -36552549980897045514699595181548502665391559659618587536128150553039982297088, 0, -2471616932593483550143673642498647085928426759655827713990033546183972457807872, 0]. Denominators A176727(n), n=0..60: [1, 1, 3, 1, 15, 1, 21, 1, 45, 1, 33, 1, 1365, 1, 45, 1, 765, 1, 399, 1, 3465, 1, 1035, 1, 20475, 1, 189, 1, 435, 1, 7161, 1, 58905, 1, 315, 1, 959595, 1, 117, 1, 20295, 1, 148995, 1, 108675, 1, 14805, 1, 2436525, 1, 65637, 1, 78705, 1, 21945, 1, 24795, 1, 531, 1]. ############################################################# e.o.f.###################################################################################################