A298610 Triangle read by rows, the unsigned coefficients of G(n, n, x/2) where G(n,a,x) denotes the n-th Gegenbauer polynomial, T(n, k) for 0 <= k <= n.

1, 0, 1, 2, 0, 3, 0, 12, 0, 10, 10, 0, 60, 0, 35, 0, 105, 0, 280, 0, 126, 56, 0, 756, 0, 1260, 0, 462, 0, 840, 0, 4620, 0, 5544, 0, 1716, 330, 0, 7920, 0, 25740, 0, 24024, 0, 6435, 0, 6435, 0, 60060, 0, 135135, 0, 102960, 0, 24310

Offset: 0

Author

Peter Luschny, Jan 25 2018

Keywords

• nonn
• tabl

Examples

			[0]   1
[1]   0,    1
[2]   2,    0,    3
[3]   0,   12,    0,    10
[4]  10,    0,   60,     0,    35
[5]   0,  105,    0,   280,     0,    126
[6]  56,    0,  756,     0,  1260,      0,   462
[7]   0,  840,    0,  4620,     0,   5544,     0,   1716
[8] 330,    0, 7920,     0, 25740,      0, 24024,      0, 6435
[9]   0, 6435,    0, 60060,     0, 135135,     0, 102960,    0,  24310
		

Crossrefs

T(2n, 0) = A165817(n). T(n,n) = A088218(n). Row sums are A213684.

Cf. A109187.

Programs

Maple

with(orthopoly):
seq(seq((-1)^iquo(n-k, 2)*coeff(G(n,n,x/2),x,k), k=0..n), n=0..9);

Mathematica

p[n_] := Binomial[3 n - 1, n] Hypergeometric2F1[-n, 3 n, n + 1/2, 1/2 - x/4];
Flatten[Table[(-1)^Floor[(n-k)/2] Coefficient[p[n], x, k], {n,0,9}, {k,0,n}]]

Formula

G(n, x) = binomial(3*n-1, n)*hypergeom([-n, 3*n], [n+1/2], 1/2 - x/4).