A361843 Expansion of 1/(1 - 9*x*(1-x))^(1/3).

1, 3, 15, 90, 585, 3969, 27657, 196290, 1411965, 10261485, 75183147, 554480316, 4111617510, 30628393110, 229048769790, 1718666596692, 12933847045701, 97584913269675, 737953856289675, 5591915004100950, 42450848142844995, 322796964495941235

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..1105

Formula

n*a(n) = 3 * ( (3*n-2)*a(n-1) - (3*n-4)*a(n-2) ) for n > 1.

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

a(n) = A004987(n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9). - Peter Luschny, Mar 27 2023

a(n) ~ 3^n * phi^(2*n + 2/3) / (Gamma(1/3) * 5^(1/6) * n^(2/3)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Mar 29 2023

Maple

A361843 := n -> (-9)^n*binomial(-1/3, n)*hypergeom([1/2 - n/2, -n/2], [2/3 - n], 4/9): seq(simplify(A361843(n)), n = 0..21); # Peter Luschny, Mar 27 2023

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-9*x*(1-x))^(1/3))

Crossrefs

Column k=1 of A361840.

Cf. A004987.

Sequence in context: A173695 A255688 A370186 * A097188 A025748 A366085

Adjacent sequences: A361840 A361841 A361842 * A361844 A361845 A361846

Keyword

nonn

Author

Seiichi Manyama, Mar 26 2023

Status

approved