A390712 a(n) = Sum_{k=0..n} (3*k+1) * binomial(5*n-2*k+1,n-k)/(5*n-2*k+1).

1, 2, 10, 69, 556, 4900, 45761, 445031, 4459282, 45720003, 477353196, 5057982974, 54251905261, 587910920213, 6427043507907, 70793456455149, 784939755671996, 8753789201898199, 98126516343926471, 1105012873683727114, 12494986616303225560, 141813698509704109440

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..920

Formula

G.f.: g/(1-x*g^3) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(3*k+1)*Binomial[5*n-2*k+1, n-k]/(5*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (3*k+1)*binomial(5*n-2*k+1, n-k)/(5*n-2*k+1));
(Magma) [&+[(3*k+1)*Binomial(5*n-2*k+1, n-k)/(5*n-2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 17 2025

Crossrefs

Cf. A118969, A304979, A390711.

Cf. A002294.

Sequence in context: A123617 A325054 A391194 * A381830 A381827 A139715

Adjacent sequences: A390709 A390710 A390711 * A390713 A390714 A390715

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved