A381829 G.f. A(x) satisfies A(x) = C(x*A(x)) / (1 - x*A(x)^3), where C(x) is the g.f. of A000108.

1, 2, 12, 97, 905, 9187, 98578, 1099980, 12636101, 148449436, 1775331503, 21541303494, 264533752068, 3281596216087, 41062196808517, 517655936768189, 6568539787903369, 83827401412072474, 1075254139150601581, 13855040994605807348, 179256835556387995412, 2327788724156294034612

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A188687, A381817, A381828.

Cf. A000108, A381783.

Sequence in context: A095338 A308820 A381818 * A322717 A219538 A245897

Adjacent sequences: A381826 A381827 A381828 * A381830 A381831 A381832

Keyword

nonn

Author

Seiichi Manyama, Mar 08 2025

Status

approved