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a(n) = n! * [x^n] exp(n*(1/(1-x)^n- 1)).
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%I #12 Oct 25 2017 02:53:13

%S 1,1,28,1881,241696,50903725,15950981376,6965675824177,

%T 4044321664205824,3013398202413705561,2802908316869098624000,

%U 3183461016834811739809321,4335741846110695855971852288,6974958097518147761490109983781

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

%H Robert Israel, <a href="/A294192/b294192.txt">Table of n, a(n) for n = 0..100</a>

%p S:= series(exp(n*(1/(1-x)^n-1)),x,31):

%p seq(n!*coeff(S,x,n),n=0..30); # _Robert Israel_, Oct 24 2017

%t Table[n! SeriesCoefficient[Exp[n (1 / (1 - x)^n - 1)], {x, 0, n}], {n, 0, 20}] (* _Vincenzo Librandi_, Oct 25 2017 *)

%Y Main diagonal of A294188.

%Y Cf. A294047.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Oct 24 2017