a(n,m) tabl head (triangle) for A049029 S2(5) n\m 1 2 3 4 5 6 7 8 9 10 ... 1 1 0 0 0 0 0 0 0 0 0 2 5 1 0 0 0 0 0 0 0 0 3 45 15 1 0 0 0 0 0 0 0 4 585 255 30 1 0 0 0 0 0 0 5 9945 5175 825 50 1 0 0 0 0 0 6 208845 123795 24150 2025 75 1 0 0 0 0 7 5221125 3427515 775845 80850 4200 105 1 0 0 0 8 151412625 108046575 27478710 3363045 219450 7770 140 1 0 0 9 4996616625 3824996175 1069801425 148548330 11482695 514710 13230 180 1 0 10 184874815125 150346471275 45547251750 7011734625 619338825 33100515 1083600 21150 225 1 . . . The row sums give A049378: [1,6,61,871,15996,358891,9509641,290528316,10051973371,388433817091,...]. The alternating row sums give A145561: [1,4,31,359,5546,107249,2492701,67693534,2103854581,73651161959,...]. The first columns give A007696 (4-factorials), A145562, A145563,... ############################################ e.o.f.###########################################################