A387639 Expansion of g/(1 + x^2*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 3, 20, 132, 920, 6758, 51513, 403613, 3230794, 26307826, 217236823, 1814829574, 15311195731, 130268265792, 1116434704474, 9629298881403, 83520835407874, 728049553149422, 6374754265347525, 56041200775726795, 494454085329302530, 4376984664739285196

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 * (k+1) * binomial(4*n-7*k+1,n-2*k)/(4*n-7*k+1).

Mathematica

Table[ Sum[(-1)^k*(k+1)*Binomial[4*n-7*k+1, n-2*k]/(4*n-7*k+1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*(k+1)*binomial(4*n-7*k+1, n-2*k)/(4*n-7*k+1));
(Magma) [&+[(-1)^k*(k+1)*Binomial(4*n-7*k+1, n-2*k)/(4*n-7*k+1): k in [0..Floor(n/2)]] : n in [0..30] ]; // Vincenzo Librandi, Dec 08 2025

Crossrefs

Cf. A391323, A391325, A391327.

Cf. A002293, A390280.

Sequence in context: A138910 A000276 A216778 * A337105 A056306 A056298

Adjacent sequences: A387636 A387637 A387638 * A387640 A387641 A387642

Keyword

nonn

Author

Seiichi Manyama, Dec 07 2025

Status

approved