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

0,3

Links

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

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).

Prog

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

Crossrefs

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

Cf. A002296, A364477.

Sequence in context: A199308 A176479 A162356 * A339440 A026302 A214460

Adjacent sequences: A364473 A364474 A364475 * A364477 A364478 A364479

Keyword

nonn

Author

Seiichi Manyama, Jul 26 2023

Status

approved