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%I #21 May 24 2020 09:33:50
%S 1,4,69,5248,1107697,492911196,396643610629,522506795651464,
%T 1050188527130093313,3055485688346936896372,
%U 12353356560641179964896741,67171925010307462937573055504,478268992794023738033117638364209,4360663458863998067849091605547380428
%N 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).
%H Seiichi Manyama, <a href="/A308294/b308294.txt">Table of n, a(n) for n = 0..166</a>
%F 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
%e 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.
%t 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 *)
%o (PARI) {a(n) = sum(i=0, 3*n, i!*polcoef(sum(j=0, 3, x^j/j!)^n, i))}
%Y Row n=3 of A308292.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 19 2019