A364588 G.f. satisfies A(x) = 1/(1-x) + x^2*A(x)^4.

1, 1, 2, 5, 15, 49, 170, 613, 2275, 8629, 33301, 130333, 516077, 2063685, 8321892, 33803161, 138181521, 568031297, 2346668400, 9737766513, 40569611691, 169632827345, 711611670532, 2994165070045, 12632782541053, 53433933353885, 226540298098019

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

Prog

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

Crossrefs

Cf. A049130, A090344.

Cf. A226974, A349289, A364591.

Sequence in context: A176025 A084082 A190270 * A341342 A149939 A149940

Adjacent sequences: A364585 A364586 A364587 * A364589 A364590 A364591

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 29 2023

Status

approved