A336170 a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+3*k)!/((n-k)! * k!^4).

1, 23, 2401, 347279, 58370761, 10693893503, 2071837562929, 417449585719343, 86587926575712937, 18366152017597820303, 3965385492963153556441, 868598410928920193676023, 192552082030654661729957401, 43117650276328970463683450639, 9738695910884616220689842598481

Offset: 0

Author

Seiichi Manyama, Jul 10 2020

Keywords

• nonn

Comments

Diagonal of the rational function 1 / (1 - Sum_{k=1..4} x_k + Product_{k=1..4} x_k).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..418

Crossrefs

Column k=4 of A336169.

Cf. A082488.

Programs

Mathematica

a[n_] := Sum[(-1)^(n - k)*(n + 3*k)!/((n - k)!*k!^4), {k, 0, n}]; Array[a, 15, 0] (* Amiram Eldar, Jul 10 2020 *)

PARI

{a(n) = sum(k=0, n, (-1)^(n-k)*(n+3*k)!/((n-k)!*k!^4))}

PARI

N=20; x='x+O('x^N); Vec(sum(k=0, N, (4*k)!/k!^4*x^k/(1+x)^(4*k+1)))

Formula

G.f.: Sum_{k>=0} (4*k)!/k!^4 * x^k / (1+x)^(4*k+1).