A307351 a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} Sum_{l=1..n} (-1)^(i+j+k+l) * (i+j+k+l)!/(4!*i!*j!*k!).

0, 1, 36, 6286, 1056496, 197741887, 38987482590, 7992252465604, 1685955453442326, 363605412277403725, 79808698852014867735, 17769930438868419048744, 4003861131932651139989514, 911215485942545343663605503, 209160405405110598032066208338

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

a(n) ~ 2^(8*n + 9/2) / (1875 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Apr 04 2019

Mathematica

Table[Sum[Sum[Sum[Sum[(-1)^(i + j + k + l)*(i + j + k + l)!/(4!*i!*j!*k!*l!), {i, 1, n}], {j, 1, n}], {k, 1, n}], {l, 1, n}], {n, 0, 14}] (* Amiram Eldar, Apr 03 2019 *)

Prog

(PARI) {a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, sum(l=1, n, (-1)^(i+j+k+l)*(i+j+k+l)!/(24*i!*j!*k!*l!)))))}
(PARI) {a(n) = sum(i=4, 4*n, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^4, i))/24} \\ Seiichi Manyama, May 20 2019

Crossrefs

Cf. A144662, A307324, A307349, A307350.

Sequence in context: A275050 A222336 A291975 * A268554 A326999 A068272

Adjacent sequences: A307348 A307349 A307350 * A307352 A307353 A307354

Keyword

nonn

Author

Seiichi Manyama, Apr 03 2019

Status

approved