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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
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
0,4
FORMULA
G(n, x) = binomial(3*n-1, n)*hypergeom([-n, 3*n], [n+1/2], 1/2 - x/4).
EXAMPLE
[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
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}]]
CROSSREFS
T(2n, 0) = A165817(n). T(n,n) = A088218(n). Row sums are A213684.
Cf. A109187.
Sequence in context: A067165 A079981 A117776 * A186492 A137448 A240606
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jan 25 2018
STATUS
approved