A365178 G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x).

1, 1, 5, 30, 210, 1595, 12791, 106574, 913562, 8004861, 71375653, 645536234, 5907683486, 54605672300, 509043322720, 4780441915832, 45182744331388, 429472919087158, 4102806757542542, 39370967793387086, 379335734835510622, 3668220243145708341

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..988

Formula

a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(k,n-k)/(4*k+1) = Sum_{k=0..n} binomial(k,n-k) * A002293(k).

Prog

(PARI) a(n) = sum(k=0, n, binomial(k, n-k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Cf. A002294, A365180, A365181, A365182, A365183.

Cf. A364475, A365184.

Cf. A002293, A364987.

Sequence in context: A222050 A091122 A029587 * A001720 A361545 A051829

Adjacent sequences: A365175 A365176 A365177 * A365179 A365180 A365181

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2023

Status

approved