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%I #14 Jun 12 2020 11:42:05
%S 1,1,6,114,4168,248870,21966768,2685571560,434202400896,
%T 89679267601632,23032451508686400,7199033431349412576,
%U 2690461258552995849216,1184680716090974803461072,606986901206377433194091520,358023049940533240478842992000,240858598980174362552808566194176
%N a(n) = n! * [x^n] 1/(1 - n*log(1 + x)).
%H Seiichi Manyama, <a href="/A317172/b317172.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=0..n} Stirling1(n,k)*n^k*k!.
%F a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n + 1/2). - _Vaclav Kotesovec_, Jul 23 2018
%t Table[n! SeriesCoefficient[1/(1 - n Log[1 + x]), {x, 0, n}], {n, 0, 16}]
%t Join[{1}, Table[Sum[StirlingS1[n, k] n^k k!, {k, n}], {n, 16}]]
%o (PARI) {a(n) = sum(k=0, n, k!*n^k*stirling(n, k, 1))} \\ _Seiichi Manyama_, Jun 12 2020
%Y Cf. A006252, A088501, A094420, A242817, A317171.
%Y Main diagonal of A320080.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 23 2018
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