%I #15 May 24 2019 12:39:31

%S 1,-1,5,-120,6286,-557991,74741031,-14055359935,3529670102365,

%T -1140712320228976,461095707510195836,-227895625979289345441,

%U 135204234793000554759865,-94817763471081620680039785,77590302489065260867070145321,-73270395178157034753637372218736

%N a(n) = (1/n!) * Sum_{i_1=1..3} Sum_{i_2=1..3} ... Sum_{i_n=1..3} (-1)^(i_1 + i_2 + ... + i_n) * multinomial(i_1 + i_2 + ... + i_n; i_1, i_2, ..., i_n).

%H Seiichi Manyama, <a href="/A308363/b308363.txt">Table of n, a(n) for n = 0..222</a>

%e a(2) = (1/2) * (binomial(1+1,1) - binomial(1+2,2) + binomial(1+3,3) - binomial(2+1,1) + binomial(2+2,2) - binomial(2+3,3) + binomial(3+1,1) - binomial(3+2,2) + binomial(3+3,3)) = 5.

%o (PARI) {a(n) = sum(i=n, 3*n, (-1)^i*i!*polcoef(sum(j=1, 3, x^j/j!)^n, i))/n!}

%Y Row n=3 of A308356.

%Y Cf. A144416.

%K sign

%O 0,3

%A _Seiichi Manyama_, May 22 2019