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%I #18 May 20 2019 15:24:57
%S 0,1,36,6286,1056496,197741887,38987482590,7992252465604,
%T 1685955453442326,363605412277403725,79808698852014867735,
%U 17769930438868419048744,4003861131932651139989514,911215485942545343663605503,209160405405110598032066208338
%N 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!).
%F a(n) ~ 2^(8*n + 9/2) / (1875 * Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Apr 04 2019
%t 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 *)
%o (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!)))))}
%o (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
%Y Cf. A144662, A307324, A307349, A307350.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 03 2019