A391605 Expansion of g^3/(1 + x*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 12, 73, 497, 3587, 27001, 209591, 1665646, 13485312, 110833730, 922316562, 7755716261, 65800033320, 562548456031, 4841654246934, 41915639949437, 364767096232883, 3189101901648337, 27998052592334464, 246727558875994408, 2181655758213023219

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(-1)^k*(k+3)*Binomial[4*n-3*k+3, n-k]/(4*n-3*k+3), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 18 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+3)*binomial(4*n-3*k+3, n-k)/(4*n-3*k+3));
(Magma) [&+[(-1)^k*(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 18 2025

Crossrefs

Cf. A387982, A391378.

Cf. A391606, A391607.

Cf. A002293, A390810.

Sequence in context: A328946 A037515 A037718 * A342054 A020049 A020004

Adjacent sequences: A391602 A391603 A391604 * A391606 A391607 A391608

Keyword

nonn

Author

Seiichi Manyama, Dec 14 2025

Status

approved