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%I #18 May 21 2019 11:34:51
%S 1,0,3,-692,25413205,-247578134832564,1049539393188856278390451,
%T -2871690441592604257533055860715129272,
%U 7040796701370550878156702345258827433898638874681737,-20490586759699718697495728993626502030472234718733294544426997558792280
%N a(n) = Sum_{i_1=0..n} Sum_{i_2=0..n} ... Sum_{i_n=0..n} (-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="/A308323/b308323.txt">Table of n, a(n) for n = 0..26</a>
%o (PARI) {a(n) = sum(i=0, n^2, (-1)^i*i!*polcoef(sum(j=0, n, x^j/j!)^n, i))}
%Y Main diagonal of A308322.
%Y Cf. A274762.
%K sign
%O 0,3
%A _Seiichi Manyama_, May 20 2019