A308296 a(n) = (1/n!) * Sum_{i_1=1..n} Sum_{i_2=1..n} ... Sum_{i_n=1..n} multinomial(i_1+i_2+...+i_n; i_1, i_2, ... , i_n).

1, 1, 7, 842, 7958726, 15467641899285, 10893033763705794846727, 4247805448772073978048752721163278, 1299618941291522676629215597535104557826094801396, 419715170056359079715862408734598208208707081189266290220651371206

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..27

Formula

a(n) = A144510(n,n).

a(n) ~ exp(n + 11/12) * n^(n^2 - 3*n/2 + 1/2) / (2*Pi)^(n/2). - Vaclav Kotesovec, Feb 15 2026

Example

a(2) = (1/2) * (binomial(1+1,1) + binomial(1+2,2) + binomial(2+1,1) + binomial(2+2,2)) = 7.

Mathematica

Join[{1}, Table[1/n! * Sum[m! * SeriesCoefficient[(E^x * Gamma[n+1, x]/Gamma[n+1] - 1)^n, {x, 0, m}], {m, n, n^2}], {n, 1, 10}]] (* Vaclav Kotesovec, Feb 13 2026 *)

Prog

(PARI) {a(n) = sum(i=n, n^2, i!*polcoef(sum(j=1, n, x^j/j!)^n, i))/n!}

Crossrefs

Cf. A144510, A144512, A274762, A281901.

Sequence in context: A203694 A269896 A087350 * A193342 A298301 A332187

Adjacent sequences: A308293 A308294 A308295 * A308297 A308298 A308299

Keyword

nonn

Author

Seiichi Manyama, May 19 2019

Status

approved