A390572 a(n) = Sum_{k=0..n} (-1)^k * binomial(5*n+k,n-k).

1, 4, 35, 351, 3724, 40755, 454895, 5147209, 58828483, 677546442, 7851048919, 91422694181, 1068927876289, 12540924304952, 147563312978648, 1740688398207816, 20578658427267084, 243753852391111981, 2892204330391503674, 34369210668523749076, 408983272598312218925

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Formula

G.f.: 1/((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} binomial(3*n+2*k-2,k).

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

Mathematica

Table[Sum[(-1)^k*Binomial[5*n+k, n-k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 11 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(5*n+k, n-k));
(Magma) [&+[(-1)^k*Binomial(5*n+k, n-k): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Nov 11 2025

Crossrefs

Cf. A279561, A390570, A390571.

Cf. A002294.

Sequence in context: A292190 A026304 A215541 * A386979 A104456 A277868

Adjacent sequences: A390569 A390570 A390571 * A390573 A390574 A390575

Keyword

nonn

Author

Seiichi Manyama, Nov 10 2025

Status

approved