A390476 a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (6*k+1) * binomial(2*n-4*k+1,n-5*k)/(2*n-4*k+1).

1, 1, 2, 5, 14, 41, 125, 394, 1276, 4225, 14249, 48803, 169356, 594337, 2106112, 7526678, 27098673, 98206226, 357980257, 1311713185, 4828900696, 17852097526, 66250699580, 246719121941, 921713219252, 3453462774565, 12974133874235, 48862615196046

Offset

0,3

Links

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

Formula

G.f.: g/(1+x^5*g^6) where g = 1+x*g^2 is the g.f. of A000108.

Mathematica

Table[Sum[(-1)^k*(6*k+1)*Binomial[2*n-4*k+1, n-5*k]/(2*n-4*k+1), {k, 0, Floor[n/5]}], {n, 0, 30}] (* Vincenzo Librandi, Nov 08 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\5, (-1)^k*(6*k+1)*binomial(2*n-4*k+1, n-5*k)/(2*n-4*k+1));
(Magma) [&+[(-1)^k*(6*k+1)*Binomial(2*n-4*k+1, n-5*k)/(2*n-4*k+1): k in [0..Floor(n/5)]] : n in [0..30] ]; // Vincenzo Librandi, Nov 08 2025

Crossrefs

Cf. A059019, A135310, A390477.

Cf. A000108.

Sequence in context: A356698 A036766 A366024 * A222589 A243870 A287968

Adjacent sequences: A390473 A390474 A390475 * A390477 A390478 A390479

Keyword

nonn

Author

Seiichi Manyama, Nov 07 2025

Status

approved