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 A318616 a(n) = n! * [x^n] (1 - x)^(n*x). 1

%I

%S 1,0,-4,-9,160,1350,-14904,-335160,1796096,125615448,204300000,

%T -64591072920,-735003528192,41673388751280,1113912529707264,

%U -30043364514345000,-1703374149711298560,17822402097051182400,2856178489894627203072,12394040043610922716800,-5255899207995216384000000

%N a(n) = n! * [x^n] (1 - x)^(n*x).

%F a(n) = n! * [x^n] exp(-n*x*Sum_{k>=1} x^k/k).

%F a(n) = n! * Sum_{k=0..n} (-1)^k*n^(n-k)*Stirling1(k,n-k)/k!.

%t Table[n! SeriesCoefficient[(1 - x)^(n x), {x, 0, n}], {n, 0, 20}]

%t Join[{1}, Table[n! Sum[(-1)^k n^(n - k) StirlingS1[k, n - k]/k!, {k, n}], {n, 20}]]

%Y Cf. A007114, A008275, A318615.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Aug 30 2018

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)