a(n,m) tabl head (triangle) for A127675 Chebyshev U-polynomials U(2*n,x) coefficients, decreasing powers of 1-x^2. n\m 0 1 2 3 4 5 6 7 8 9 10 0 1 0 0 0 0 0 0 0 0 0 0 1 -4 3 0 0 0 0 0 0 0 0 0 2 16 -20 5 0 0 0 0 0 0 0 0 3 -64 112 -56 7 0 0 0 0 0 0 0 4 256 -576 432 -120 9 0 0 0 0 0 0 5 -1024 2816 -2816 1232 -220 11 0 0 0 0 0 6 4096 -13312 16640 -9984 2912 -364 13 0 0 0 0 7 -16384 61440 -92160 70400 -28800 6048 -560 15 0 0 0 8 65536 -278528 487424 -452608 239360 -71808 11424 -816 17 0 0 9 -262144 1245184 -2490368 2723840 -1770496 695552 -160512 20064 -1140 19 0 10 1048576 -5505024 12386304 -15597568 12042240 -5870592 1793792 -329472 33264 -1540 21 . . . The rows for n=11..15 are: n=11: [-4194304, 24117248, -60293120, 85917696, -76873728, 44843008, -17145856, \ 4209920, -631488, 52624, -2024, 23], n=12: [16777216, -104857600, 288358400, -458752000, 466944000, -317521920, \ 146227200, -45260800, 9152000, -1144000, 80080, -2600, 25], n=13: [-67108864, 452984832, -1358954496, 2387607552, -2724986880, 2118057984, \ -1143078912, 428654592, -109983744, 18670080, -1976832, 117936, -3276, 27], n=14: [-67108864, 452984832, -1358954496, 2387607552, -2724986880, 2118057984, \ -1143078912, 428654592, -109983744, 18670080, -1976832, 117936, -3276, 27], n=15: [-1073741824, 8321499136, -29125246976, 60850962432, -84515225600, \ 82239815680, -57567870976, 29297934336, -10827497472, 2870927360, -533172224, \ 66646528, -5261568, 236096, -4960, 31]. Row sums give (signed) A033999(n)=(-1)^n and (unsigned) A002315(n)=[1, 7, 41, 239, 1393, 8119, 47321, 275807, 1607521,...]. ######################################## e.o.f. ###########################################################