A371787 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(5*n-k,n-2*k).

1, 5, 44, 441, 4675, 51129, 570401, 6451688, 73715212, 848793726, 9833394285, 114487194485, 1338411363535, 15700659542105, 184722993467063, 2178831068873601, 25756348168285379, 305061478075705411, 3619402085862708614, 43008294559624639777

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..921

Formula

a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(4*n)).

It appears that a(n) = Sum_{k = 0..n} binomial(3*n+2*k-1, k). - Peter Bala, Jun 04 2024

From Seiichi Manyama, Nov 10 2025: (Start)

G.f.: g/((1-5*x*g^4) * (1+x*g^6)) where g = 1+x*g^5 is the g.f. of A002294.

a(n) = Sum_{k=0..n} (-1)^k * binomial(5*n+k+1,n-k). (End)

Mathematica

Table[Sum[(-1)^k Binomial[5n-k, n-2k], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Harvey P. Dale, Nov 16 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(5*n-k, n-2*k));

Crossrefs

Cf. A024718, A371785, A371786.

Cf. A002294, A371744.

Sequence in context: A374300 A227640 A096355 * A222508 A220841 A366924

Adjacent sequences: A371784 A371785 A371786 * A371788 A371789 A371790

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 06 2024

Status

approved