A391455 Expansion of g^2/(1 + x^2*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 8, 48, 319, 2260, 16779, 128900, 1016128, 8173562, 66821750, 553612116, 4637917939, 39222516270, 334397941985, 2871064642908, 24802493457353, 215431230581288, 1880279781321079, 16482275179530108, 145046018462347290, 1280937845033086008

Offset

0,2

Links

Vincenzo Librandi, 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-6*k+2,n-2*k)/(2*n-3*k+1).

Mathematica

Table[Sum[(-1)^k*(k+1)*Binomial[4*n-6*k+2, n-2*k]/(2*n-3*k+1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*(k+1)*binomial(4*n-6*k+2, n-2*k)/(2*n-3*k+1));
(Magma) [&+[(-1)^k*(k+1)*Binomial(4*n-6*k+2, n-2*k)/(2*n-3*k+1): k in [0..Floor(n/2)]] : n in [0..25] ]; // Vincenzo Librandi, Dec 20 2025

Crossrefs

Cf. A002293, A390147.

Sequence in context: A152661 A177066 A356429 * A228568 A007170 A355488

Adjacent sequences: A391452 A391453 A391454 * A391456 A391457 A391458

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved