A364594 G.f. satisfies A(x) = 1/(1-x) + x^2*(1-x)*A(x)^4.

1, 1, 2, 4, 11, 31, 98, 316, 1065, 3649, 12775, 45299, 162713, 590097, 2159015, 7957003, 29517141, 110116277, 412879256, 1555048142, 5880591163, 22319380999, 84992915958, 324634976440, 1243396473153, 4774504667881, 18376620653851, 70883537152927

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

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

Prog

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

Crossrefs

Cf. A110199, A364593.

Cf. A364592, A364596.

Sequence in context: A073191 A173139 A148164 * A213091 A148165 A148166

Adjacent sequences: A364591 A364592 A364593 * A364595 A364596 A364597

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved