A364826 G.f. satisfies A(x) = 1 - x*A(x)^4 * (1 - 3*A(x)).

1, 2, 22, 338, 6038, 117570, 2420758, 51833106, 1142472150, 25749801986, 590737764118, 13748997055826, 323842714201622, 7704914865207362, 184899022770465558, 4470200057557410834, 108776308617293352534, 2662072268791363675650

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..704

Formula

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

a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(5*n-k,n-1-k) for n > 0.

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

Prog

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

Crossrefs

Cf. A025192, A107841, A235347, A364825, A364827.

Cf. A243667, A260332.

Sequence in context: A266888 A155674 A279619 * A245113 A363006 A363304

Adjacent sequences: A364823 A364824 A364825 * A364827 A364828 A364829

Keyword

nonn

Author

Seiichi Manyama, Aug 09 2023

Status

approved