A372137 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1 + 9*x)^(1/3) * A(x)^2 ).

1, 1, 6, 21, 181, 771, 7728, 34689, 385632, 1732971, 21041598, 92147697, 1217109951, 5099210686, 73380609681, 289623783084, 4564472639880, 16722146775195, 290985244619874, 974044248064611, 18925364858562927, 56848541164586820, 1251693011560795635

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..n} 9^(n-k) * binomial(3*k,k) * binomial(k/3,n-k)/(2*k+1).

Prog

(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(3*k, k)*binomial(k/3, n-k)/(2*k+1));

Crossrefs

Cf. A364475, A372139.

Cf. A372124.

Sequence in context: A210443 A179768 A131960 * A244299 A143049 A213680

Adjacent sequences: A372132 A372135 A372136 * A372138 A372139 A372140

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2024

Status

approved