A391606 Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 10, 58, 403, 2924, 22113, 172213, 1372044, 11130261, 91624156, 763466227, 6427041731, 54578677149, 466990198097, 4022044368331, 34841523036049, 303370789888274, 2653614010505109, 23307012085832216, 205469444942615266, 1817484106437134810

Offset

0,3

Links

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

Formula

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

Mathematica

Table[Sum[(-1)^k*(k+1)*(k+3)*Binomial[4*n-3*k+3, n-k]/(4*n-3*k+3), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 19 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+1)*(k+3)*binomial(4*n-3*k+3, n-k)/(4*n-3*k+3));
(Magma) [&+[(-1)^k*(k+1)*(k+3)*Binomial(4*n-3*k+3, n-k)/(4*n-3*k+3): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 19 2025

Crossrefs

Cf. A002293, A391277.

Sequence in context: A321112 A126730 A126478 * A223470 A044148 A044529

Adjacent sequences: A391603 A391604 A391605 * A391607 A391608 A391609

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2025

Status

approved