A307350 a(n) = -Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} (-1)^(i+j+k) * (i+j+k)!/(3!*i!*j!*k!).

0, 1, -5, 120, -2380, 52556, -1192625, 27798310, -660128942, 15907062666, -387785597485, 9543399745815, -236715891871160, 5910596888393926, -148421725618783545, 3745355227481531010, -94917946415633366050, 2414582011729590475886

Offset: 0

Author

Seiichi Manyama, Apr 03 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A144511, A307318, A307349, A307351.

Programs

Mathematica

Table[-Sum[Sum[Sum[(-1)^(i + j + k)*(i + j + k)!/(3!*i!*j!*k!), {i, 1, n}], {j, 1, n}], {k, 1, n}], {n, 0, 17}] (* Amiram Eldar, Apr 03 2019 *)

PARI

{a(n) = -sum(i=1, n, sum(j=1, n, sum(k=1, n, (-1)^(i+j+k)*(i+j+k)!/(6*i!*j!*k!))))}

PARI

{a(n) = -sum(i=3, 3*n, (-1)^i*i!*polcoef(sum(j=1, n, x^j/j!)^3, i))/6} \\ Seiichi Manyama, May 20 2019

Formula

a(n) ~ -(-1)^n * 3^(3*n + 5/2) / (256*Pi*n). - Vaclav Kotesovec, Apr 04 2019