A361638 Expansion of g.f. A(x) satisfying A(x) = 1 + x * A(x)^2 * (1 + A(x)^3).

1, 2, 14, 142, 1690, 21994, 303126, 4348102, 64235570, 970695442, 14934154334, 233133082494, 3683546302538, 58794776161274, 946619511627622, 15355445768326710, 250717346336174690, 4117189670041072930, 67956239699290313646, 1126763233375565370990

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2*n+3*k+1,n)/(2*n+3*k+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(2*n+3*k+1, n)/(2*n+3*k+1));

Crossrefs

Cf. A027307, A219534.

Sequence in context: A301271 A245267 A328004 * A271564 A100510 A354290

Adjacent sequences: A361635 A361636 A361637 * A361639 A361640 A361641

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 13 2023

Status

approved