A361896 Expansion of 1/(1 - 9*x/(1 - x)^4)^(1/3).

1, 3, 30, 300, 3165, 34584, 386880, 4400928, 50692266, 589584042, 6910397886, 81507086634, 966408021984, 11509174498254, 137584249375308, 1650109151463594, 19847075122106145, 239316542492974317, 2892135259684291248, 35021199836282568456, 424837125616822551264

Offset: 0

Author

Seiichi Manyama, Mar 28 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..907

Crossrefs

Cf. A004987, A361375, A361843, A361844, A361845, A361880, A361895.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/(1-9*x/(1-x)^4)^(1/3))

Formula

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

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