A361847 a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(n*k,n-k).

1, 3, 12, 27, -75, -444, 4734, 11532, -466782, 1626750, 50347410, -708889296, -2196754992, 179878246239, -1795732735128, -24691325878980, 953903679982809, -7684914725016600, -226465559200630566, 7742131606464606525, -58889021552013912990

Offset

0,2

Links

Winston de Greef, Table of n, a(n) for n = 0..468

Formula

a(n) = [x^n] 1/(1 - 9*x*(1-x)^n)^(1/3).

Prog

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

Crossrefs

Main diagonal of A361840.

Cf. A361835, A361846.

Sequence in context: A058034 A294416 A187273 * A009259 A183503 A216713

Adjacent sequences: A361844 A361845 A361846 * A361848 A361849 A361850

Keyword

sign

Author

Seiichi Manyama, Mar 27 2023

Status

approved