A377233 Expansion of 1/(1 - 9*x/(1-x))^(2/3).

1, 6, 51, 456, 4191, 39174, 370329, 3529284, 33838854, 325978044, 3152058630, 30572797920, 297294956070, 2897207397420, 28286321963370, 276611636831640, 2708781551458665, 26559205696513590, 260695647288540915, 2561413004129212440, 25188928968792165495

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = 3 * Sum_{k=0..n-1} (2+k/n) * a(k).

a(n) = ((11*n-5)*a(n-1) - 10*(n-2)*a(n-2))/n for n > 1.

a(n) = Sum_{k=0..n} (-9)^k * binomial(-2/3,k) * binomial(n-1,n-k).

a(n) ~ Gamma(1/3) * 3^(11/6) * 2^(n - 5/3) * 5^(n - 2/3) / (Pi * n^(1/3)). - Vaclav Kotesovec, Oct 21 2024

Prog

(PARI) a(n) = sum(k=0, n, (-9)^k*binomial(-2/3, k)*binomial(n-1, n-k));

Crossrefs

Cf. A052268, A361375, A377234, A377235.

Sequence in context: A011790 A292840 A356394 * A202754 A363112 A180901

Adjacent sequences: A377230 A377231 A377232 * A377234 A377235 A377236

Keyword

nonn

Author

Seiichi Manyama, Oct 21 2024

Status

approved