A307324 a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} Sum_{l=0..n} (-1)^(i+j+k+l) * (i+j+k+l)!/(i!*j!*k!*l!).

1, 9, 997, 148041, 25413205, 4744544613, 935728207597, 191813392024137, 40462946725744501, 8726529512888314245, 1915408781755211655133, 426478330303800465141669, 96092667172064808771832957, 21869171662479233922632691261

Offset: 0

Author

Seiichi Manyama, Apr 02 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400
• Vaclav Kotesovec, Recurrence (of order 5)

Crossrefs

Cf. A120305, A144661, A307318.

Programs

Mathematica

Table[Sum[(-1)^(i + j + k + l) * (i + j + k + l)! / (i!*j!*k!*l!), {i, 0, n}, {j, 0, n}, {k, 0, n}, {l, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2019 *)
Table[Sum[((-1)^(j + k + l) * 2^(-1 - j - k - l) * ((j + k + l)! * (1 + n)! + (-1)^n * 2^(1 + j + k + l) * (1 + j + k + l + n)! Hypergeometric2F1[1, 2 + j + k + l + n, 2 + n, -1]))/(j! k! l! (1 + n)!), {j, 0, n}, {k, 0, n}, {l, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 03 2019 *)

PARI

{a(n) = sum(i=0, n, sum(j=0, n, sum(k=0, n, sum(l=0, n, (-1)^(i+j+k+l)*(i+j+k+l)!/(i!*j!*k!*l!)))))}

PARI

{a(n) = sum(i=0, 4*n, (-1)^i*i!*polcoef(sum(j=0, n, x^j/j!)^4, i))} \\ Seiichi Manyama, May 20 2019

Formula

a(n) ~ 2^(8*n + 15/2) / (625 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Apr 03 2019