A364403 G.f. A(x) satisfies A(x) = 1 + x^4 * (A(x) / (1 - x))^3.

1, 0, 0, 0, 1, 3, 6, 10, 18, 39, 91, 204, 435, 919, 1992, 4434, 9947, 22215, 49455, 110480, 248505, 561930, 1273610, 2889666, 6566736, 14959083, 34163511, 78182700, 179201199, 411325125, 945512784, 2176710450, 5018195400, 11583688995, 26770164919

Offset

0,6

Links

Table of n, a(n) for n=0..34.

Formula

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

Prog

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

Crossrefs

Partial sums give A364552.

Cf. A000245, A213282, A361932.

Sequence in context: A029864 A075111 A080014 * A360892 A132274 A253768

Adjacent sequences: A364400 A364401 A364402 * A364404 A364405 A364406

Keyword

nonn

Author

Seiichi Manyama, Oct 15 2023

Status

approved