A364866 G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^5).

1, 1, 4, 21, 124, 781, 5120, 34474, 236492, 1644222, 11543644, 81623504, 580104672, 4137414963, 29574658416, 211639869236, 1514729242092, 10832683182538, 77342204972120, 550791674067623, 3908735530965604, 27612614422978557, 193943797650498016

Offset: 0

Author

Seiichi Manyama, Aug 11 2023

Keywords

• sign

Comments

a(34) is negative.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A291534, A364864, A364865, A365218.

Cf. A002295.

Programs

PARI

a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(5*n+k+1, n)/(5*n+k+1));

Formula

a(n) = Sum_{k=0..n} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(5*n+k+1,n) / (5*n+k+1).

a(n) = (1/n) * Sum_{k=0..n-1} (-2)^k * binomial(n,k) * binomial(6*n-k,n-1-k) for n > 0.

a(n) = (1/n) * Sum_{k=1..n} (-1)^(n-k) * binomial(n,k) * binomial(5*n,k-1) for n > 0.