A390527 a(n) = Sum_{k=0..n} (4*k+1) * binomial(2*n+2*k+1,n-k)/(2*n+2*k+1).

1, 2, 8, 35, 157, 712, 3248, 14869, 68222, 313487, 1441999, 6637879, 30572032, 140860379, 649202036, 2992721902, 13798302512, 63626933527, 293426802548, 1353295096618, 6241829542241, 28790709824587, 132803515725281, 612604408102432, 2825929675569155

Offset

0,2

Links

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

Formula

G.f.: g/(1-x*g^4) where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[(4*k+1)*Binomial[2*n+2*k+1, n-k]/(2*n+2*k+1), {k, 0, n}], {n, 0, 22}] (* Vincenzo Librandi, Nov 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (4*k+1)*binomial(2*n+2*k+1, n-k)/(2*n+2*k+1));
(Magma) [&+[(4*k+1)*Binomial(2*n+2*k+1, n-k)/(2*n+2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 12 2025

Crossrefs

Cf. A026726, A390528.

Cf. A000108.

Sequence in context: A037618 A326294 A184786 * A082759 A243204 A279013

Adjacent sequences: A390524 A390525 A390526 * A390528 A390529 A390530

Keyword

nonn

Author

Seiichi Manyama, Nov 09 2025

Status

approved