A308294 a(n) = Sum_{i_1=0..3} Sum_{i_2=0..3} ... Sum_{i_n=0..3} multinomial(i_1+i_2+...+i_n; i_1, i_2, ... , i_n).

1, 4, 69, 5248, 1107697, 492911196, 396643610629, 522506795651464, 1050188527130093313, 3055485688346936896372, 12353356560641179964896741, 67171925010307462937573055504, 478268992794023738033117638364209, 4360663458863998067849091605547380428

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..166

Formula

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

Example

a(2) = binomial(0+0,0) + binomial(0+1,1) + binomial(0+2,2) + binomial(0+3,3) + binomial(1+0,0) + binomial(1+1,1) + binomial(1+2,2) + binomial(1+3,3) + binomial(2+0,0) + binomial(2+1,1) + binomial(2+2,2) + binomial(2+3,3) + binomial(3+0,0) + binomial(3+1,1) + binomial(3+2,2) + binomial(3+3,3) = 69.

Mathematica

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

Prog

(PARI) {a(n) = sum(i=0, 3*n, i!*polcoef(sum(j=0, 3, x^j/j!)^n, i))}

Crossrefs

Row n=3 of A308292.

Sequence in context: A248027 A093852 A065573 * A278553 A101841 A274873

Adjacent sequences: A308291 A308292 A308293 * A308295 A308296 A308297

Keyword

nonn

Author

Seiichi Manyama, May 19 2019

Status

approved