A358502 Triangle read by rows. The coefficients of the polynomials hypergeom([-x, -x, -n], [-x - n, -x - n], 1) * Product_{j=1..n} (j + x)^2 in ascending order of powers.

1, 1, 2, 4, 12, 12, 36, 132, 180, 120, 576, 2400, 4080, 3360, 1680, 14400, 65760, 126000, 134400, 75600, 30240, 518400, 2540160, 5382720, 6350400, 4838400, 1995840, 665280, 25401600, 131725440, 299315520, 396688320, 325987200, 190935360, 60540480, 17297280

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Example

Triangle T(n, k) starts:
[0]      1;
[1]      1,       2;
[2]      4,      12,      12;
[3]     36,     132,     180,     120;
[4]    576,    2400,    4080,    3360,    1680;
[5]  14400,   65760,  126000,  134400,   75600,   30240;
[6] 518400, 2540160, 5382720, 6350400, 4838400, 1995840, 665280;

Maple

p := (n, x) -> hypergeom([-x, -x, -n], [-x - n, -x - n], 1)*mul((j + x)^2, j=1..n): for n from 0 to 7 do seq(coeff(simplify(p(n, x)), x, k), k = 0..n) od;

Crossrefs

Sequence in context: A309515 A375551 A342311 * A141668 A087796 A268494

Adjacent sequences: A358499 A358500 A358501 * A358503 A358504 A358505

Keyword

nonn,tabl

Author

Peter Luschny, Nov 26 2022

Status

approved