A307318 a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).

1, -2, 37, -692, 14371, -315002, 7156969, -166785320, 3960790687, -95442311582, 2326713829837, -57260397539204, 1420295354815351, -35463581316556850, 890530353765972817, -22472131364683145552, 569507678494598796631, -14487492070374441746150

Offset

0,2

Links

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

Formula

From Vaclav Kotesovec, Apr 02 2019: (Start)

Recurrence: 6*(n-1)*n^2*(490*n^4 - 3948*n^3 + 11668*n^2 - 14967*n + 7027)*a(n) = - (n-1)*(74480*n^6 - 675066*n^5 + 2399756*n^4 - 4233492*n^3 + 3852029*n^2 - 1682577*n + 272160)*a(n-1) + (131320*n^7 - 1437814*n^6 + 6472114*n^5 - 15414556*n^4 + 20770423*n^3 - 15610855*n^2 + 5939868*n - 861840)*a(n-2) - (27440*n^7 - 355838*n^6 + 1853810*n^5 - 4998800*n^4 + 7460459*n^3 - 6071312*n^2 + 2439561*n - 362880)*a(n-3) - 3*(2*n - 5)*(3*n - 8)*(3*n - 7)*(490*n^4 - 1988*n^3 + 2764*n^2 - 1515*n + 270)*a(n-4).

a(n) ~ (-1)^n * 3^(3*n + 7/2) / (128*Pi*n). (End)

Mathematica

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

Prog

(PARI) {a(n) = sum(i=0, n, sum(j=0, n, sum(k=0, n, (-1)^(i+j+k)*(i+j+k)!/(i!*j!*k!))))}
(PARI) {a(n) = sum(i=0, 3*n, (-1)^i*i!*polcoef(sum(j=0, n, x^j/j!)^3, i))} \\ Seiichi Manyama, May 20 2019

Crossrefs

Cf. A120305, A144660, A307324.

Sequence in context: A216539 A139122 A123216 * A058245 A257995 A234971

Adjacent sequences: A307315 A307316 A307317 * A307319 A307320 A307321

Keyword

sign

Author

Seiichi Manyama, Apr 02 2019

Status

approved