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a(n) = (n!)^n * Sum_{k=0..n} (-1)^k / (k!)^n.
1

%I #8 Jul 14 2020 21:39:41

%S 1,0,1,26,20481,774403124,2173797080953345,645067515585218711490294,

%T 27280857986486289638369834192338945,

%U 213095986405176211170558965907644717041658073416,386654453940903446694477049963665295677203885863801760000000001

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

%t Table[(n!)^n Sum[(-1)^k/(k!)^n, {k, 0, n}], {n, 0, 10}]

%o (PARI) a(n) = (n!)^n * sum(k=0, n, (-1)^k / (k!)^n); \\ _Michel Marcus_, Jul 14 2020

%Y Cf. A000166, A036740, A073701, A336247.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Jul 14 2020