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a(n) = [x^n] 1/(Sum_{k=0..n} (k!)^n * x^k).
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%I #9 Mar 05 2019 01:53:40

%S 1,-1,-3,-201,-328975,-24866803361,-139308071489312831,

%T -82606210548424879390169217,-6984963414431972003347406551951687935,

%U -109110687852301656115645192848607902864427297823233

%N a(n) = [x^n] 1/(Sum_{k=0..n} (k!)^n * x^k).

%H Seiichi Manyama, <a href="/A306630/b306630.txt">Table of n, a(n) for n = 0..30</a>

%Y Main diagonal of A306629.

%K sign

%O 0,3

%A _Seiichi Manyama_, Mar 02 2019