A391327 Expansion of g/(1 + x^2*g^6), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 3, 15, 92, 625, 4518, 34067, 264876, 2108122, 17089955, 140620685, 1171370236, 9858740030, 83708026208, 716151866019, 6167531084156, 53424291896860, 465157370556204, 4068682850990824, 35735239228966952, 315031802838535433, 2786616050168401350

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (6*k+1) * binomial(4*n-2*k+1,n-2*k)/(4*n-2*k+1).

a(n) = (1/(3*n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * (6*k+1) * binomial(4*n-2*k,n-2*k).

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

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

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*(6*k+1)*binomial(4*n-2*k+1, n-2*k)/(4*n-2*k+1));

Crossrefs

Cf. A387639, A391323, A391325.

Cf. A002293, A391104, A391306.

Sequence in context: A124553 A391103 A369623 * A366053 A369114 A020108

Adjacent sequences: A391324 A391325 A391326 * A391328 A391329 A391330

Keyword

nonn

Author

Seiichi Manyama, Dec 07 2025

Status

approved