A390721 a(n) = Sum_{k=0..n} (k+2) * binomial(5*n-4*k+2,n-k)/(5*n-4*k+2).

1, 3, 15, 103, 833, 7381, 69276, 676555, 6802814, 69949499, 732099536, 7773188813, 83521931171, 906478836870, 9922793839711, 109426668183175, 1214551788118680, 13557416935589156, 152099318341418174, 1714087810020632151, 19395280422854560090, 220265616659410691342

Offset

0,2

Links

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

Formula

G.f.: g^2/(1-x*g) where g = 1+x*g^5 is the g.f. of A002294.

Mathematica

Table[Sum[(k+2)*Binomial[5*n-4*k+2, n-k]/(5*n-4*k+2), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+2)*binomial(5*n-4*k+2, n-k)/(5*n-4*k+2));
(Magma) [&+[(k+2)*Binomial(5*n-4*k+2, n-k)/(5*n-4*k+2): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 16 2025

Crossrefs

Cf. A000245, A390719, A390720.

Cf. A002294.

Sequence in context: A354122 A318618 A123184 * A079486 A245118 A372698

Adjacent sequences: A390718 A390719 A390720 * A390722 A390723 A390724

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved