A391456 Expansion of g^2/(1 + x^3*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 9, 51, 336, 2372, 17571, 134757, 1060967, 8526011, 69649968, 576686912, 4828760456, 40818936354, 347881337345, 2985889744311, 25787373559671, 223931861330691, 1954056716589431, 17125740608096079, 150682919553817883, 1330514274189243211

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (k+1) * binomial(4*n-10*k+2,n-3*k)/(2*n-5*k+1).

Mathematica

Table[Sum[(-1)^k*(k+1)*Binomial[4*n-10*k+2, n-3*k]/(2*n-5*k+1), {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 20 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(k+1)*binomial(4*n-10*k+2, n-3*k)/(2*n-5*k+1));
(Magma) [&+[(-1)^k*(k+1)*Binomial(4*n-10*k+2, n-3*k)/(2*n-5*k+1): k in [0..Floor(n/3)]] : n in [0..25] ]; //  Vincenzo Librandi, Dec 20 2025

Crossrefs

Cf. A002293, A391079.

Sequence in context: A374567 A246464 A391458 * A391454 A355397 A009310

Adjacent sequences: A391453 A391454 A391455 * A391457 A391458 A391459

Keyword

nonn

Author

Seiichi Manyama, Dec 10 2025

Status

approved