A308295 a(n) = Sum_{i_1=0..4} Sum_{i_2=0..4} ... Sum_{i_n=0..4} multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).

1, 5, 251, 110251, 191448941, 904434761801, 9459612561834055, 191593734298902552191, 6835386432791154682927481, 400218584926232312004573701101, 36402864165071086859006490971345651, 4922828438813493756340086555005103394355

Offset: 0

Author

Seiichi Manyama, May 19 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..129

Crossrefs

Row n=4 of A308292.

Programs

Mathematica

Table[Total[CoefficientList[Series[(1 + x + x^2/2 + x^3/6 + x^4/24)^n, {x, 0, 4*n}], x] * Range[0, 4*n]!], {n, 0, 15}] (* Vaclav Kotesovec, May 24 2020 *)

PARI

{a(n) = sum(i=0, 4*n, i!*polcoef(sum(j=0, 4, x^j/j!)^n, i))}

Formula

a(2) = binomial(0+0,0) + binomial(0+1,1) + binomial(0+2,2) + binomial(0+3,3) + binomial(0+4,4) + binomial(1+0,0) + binomial(1+1,1) + binomial(1+2,2) + binomial(1+3,3) + binomial(1+4,4) + binomial(2+0,0) + binomial(2+1,1) + binomial(2+2,2) + binomial(2+3,3) + binomial(2+4,4) + binomial(3+0,0) + binomial(3+1,1) + binomial(3+2,2) + binomial(3+3,3) + binomial(3+4,4) + binomial(4+0,0) + binomial(4+1,1) + binomial(4+2,2) + binomial(4+3,3) + binomial(4+4,4) = 251.

a(n) ~ sqrt(Pi) * 2^(5*n + 3/2) * n^(4*n + 1/2) / (3^n * exp(4*n - 1)). - Vaclav Kotesovec, May 24 2020