A364476 G.f. satisfies A(x) = 1 + x*A(x) + x^2*A(x)^7.

1, 1, 2, 9, 44, 226, 1241, 7093, 41666, 250260, 1529993, 9488398, 59545909, 377451385, 2413157855, 15542535697, 100753850132, 656856027658, 4303970039402, 28328599504756, 187214549485759, 1241775795647609, 8263989319451514, 55163575187733922

Offset: 0

Author

Seiichi Manyama, Jul 26 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A000045, A000108, A001006, A182454, A186996, A364472.

Cf. A002296, A364477.

Programs

PARI

a(n) = sum(k=0, n\2, binomial(n+5*k, k)*binomial(n+4*k, n-2*k)/(6*k+1));

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n+5*k,k) * binomial(n+4*k,n-2*k) / (6*k+1) = Sum_{k=0..floor(n/2)} binomial(n+5*k,7*k) * binomial(7*k,k) / (6*k+1).