A306432 a(n) = Sum_{0<=i

0, 0, 3, 77, 1777, 41088, 964199, 22962721, 553886872, 13504654074, 332253097450, 8237141855085, 205552200503455, 5158397884289338, 130087682458168777, 3294763277704155587, 83764781257030939439, 2136808562574516060202, 54674217200832983666877

Offset: 0

Author

Seiichi Manyama, Apr 05 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A057552, A307352.

Programs

Maple

g:= proc(n) local i,j;
  add(add((i+j+n)!/(i!*j!*n!),j=i+1..n-1),i=0..n-2)
end proc:
ListTools:-PartialSums(map(g,[$0..30])); # Robert Israel, May 16 2019

Mathematica

Table[Sum[Sum[Sum[(i + j + k)!/(i!*j!*k!), {i, 0, j-1}], {j, 0, k-1}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 05 2019 *)

PARI

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

Formula

a(n) ~ 3^(3*n + 7/2) / (832*Pi*n). - Vaclav Kotesovec, Apr 05 2019