A364596 G.f. satisfies A(x) = 1/(1-x) + x^3*(1-x)*A(x)^4.

1, 1, 1, 2, 4, 7, 15, 36, 82, 191, 471, 1166, 2884, 7267, 18523, 47349, 121821, 315781, 822165, 2148811, 5641035, 14864295, 39287907, 104154066, 276899112, 737984583, 1971375679, 5277570860, 14156881590, 38045460023, 102421374775, 276174537027, 745822179831

Offset

0,4

Links

Table of n, a(n) for n=0..32.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,2*k) * binomial(4*k,k) / (3*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n-k, 2*k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Cf. A364595, A364597.

Cf. A215340, A226974.

Cf. A364592, A364594.

Sequence in context: A072964 A247291 A030033 * A280031 A135131 A032363

Adjacent sequences: A364593 A364594 A364595 * A364597 A364598 A364599

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved