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Expansion of e.g.f. (1-2*x)^(-x).
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%I #19 May 21 2022 08:40:59

%S 1,0,4,12,112,960,10848,141120,2122496,36094464,685578240,14385761280,

%T 330532435968,8253827112960,222587077558272,6447285982126080,

%U 199630453605335040,6580280144225894400,230056747973625249792,8503148524089755566080

%N Expansion of e.g.f. (1-2*x)^(-x).

%H G. C. Greubel, <a href="/A053491/b053491.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) ~ 2^(n+1/2)*n^n/exp(n). - _Vaclav Kotesovec_, Jun 27 2013

%F a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * |Stirling1(n-k,k)|/(n-k)!. - _Seiichi Manyama_, May 20 2022

%t CoefficientList[Series[(1-2x)^(-x), {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)

%o (PARI) a(n) = n!*sum(k=0, n\2, 2^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!); \\ _Seiichi Manyama_, May 20 2022

%Y Cf. A007113, A053489, A066166.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 15 2000