A387982 a(n) = Sum_{k=0..n} (-1)^k * (k+1) * binomial(4*n-3*k+1,n-k)/(4*n-3*k+1).

1, 0, 3, 15, 100, 702, 5187, 39697, 312013, 2503839, 20429974, 168985397, 1413733042, 11941669508, 101705923521, 872436699540, 7530784337131, 65365039488966, 570142575501141, 4994932764558455, 43933243754844657, 387802669600452889, 3434321565780221818

Offset

0,3

Links

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

Formula

G.f.: g/(1+x*g) where g = 1+x*g^4 is the g.f. of A002293.

Mathematica

Table[Sum[(-1)^k*(k+1)*Binomial[4*n -3*k+1, n-k]/(4*n-3*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+1)*binomial(4*n-3*k+1, n-k)/(4*n-3*k+1));
(Magma) [&+[(-1)^k*(k+1)*Binomial(4*n-3*k+1, n-k)/(4*n-3*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A390500, A390740.

Cf. A023053, A390741.

Cf. A002293.

Sequence in context: A226515 A135883 A372157 * A382544 A381906 A147664

Adjacent sequences: A387979 A387980 A387981 * A387983 A387984 A387985

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved