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A383936

Expansion of 1 / ( (1-6*x) * (1+3*x)^2 )^(1/3).

1, 0, 9, 18, 162, 648, 4050, 20412, 117369, 639576, 3628233, 20360970, 115858512, 659144304, 3772679976, 21637128240, 124518397770, 718139766240, 4151542099770, 24045292507860, 139520453553468, 810834881716080, 4719151317787452, 27502373918849544

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OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

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

a(n) ~ 2^(n + 2/3) * 3^(n - 2/3) / (Gamma(1/3) * n^(2/3)). - Vaclav Kotesovec, Aug 18 2025

D-finite with recurrence n*a(n) +3*(-n+1)*a(n-1) +18*(-n+1)*a(n-2)=0. - R. J. Mathar, Aug 26 2025

MATHEMATICA

CoefficientList[Series[1/((1-6*x)*(1+3*x)^2)^(1/3), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 28 2025 *)

PROG

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

(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1 / ( (1-6*x) * (1+3*x)^2 )^(1/3); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 28 2025

CROSSREFS

Cf. A383935.

Sequence in context: A080453 A222811 A379938 * A002169 A050685 A278588

Adjacent sequences: A383933 A383934 A383935 * A383937 A383938 A383939

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Aug 18 2025

STATUS

approved

URL: https://oeis.org/A383936

⇱ A383936 - OEIS