A336171 a(n) = Sum_{k=0..n} (-1)^(n-k) * (n+4*k)!/((n-k)! * k!^5).

1, 119, 112681, 166923119, 302857024681, 616967236620839, 1354737230950753441, 3135180238488702264959, 7543003841027749147438441, 18698821633118804601271092959, 47466852090165503045193665276041, 122841260732098480578334554450553679, 323029586700918689286922557725358306721

Offset

0,2

Comments

Diagonal of the rational function 1 / (1 - Sum_{k=1..5} x_k + Product_{k=1..5} x_k).

Links

Table of n, a(n) for n=0..12.

Formula

G.f.: Sum_{k>=0} (5*k)!/k!^5 * x^k / (1+x)^(5*k+1).

Mathematica

a[n_] := Sum[(-1)^(n - k)*(n + 4*k)!/((n - k)!*k!^5), {k, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, Jul 10 2020 *)

Prog

(PARI) {a(n) = sum(k=0, n, (-1)^(n-k)*(n+4*k)!/((n-k)!*k!^5))}
(PARI) N=20; x='x+O('x^N); Vec(sum(k=0, N, (5*k)!/k!^5*x^k/(1+x)^(5*k+1)))

Crossrefs

Column k=5 of A336169.

Cf. A082489.

Sequence in context: A192726 A266032 A269123 * A349429 A196429 A243779

Adjacent sequences: A336168 A336169 A336170 * A336172 A336173 A336174

Keyword

nonn

Author

Seiichi Manyama, Jul 10 2020

Status

approved