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%I #12 Nov 15 2017 02:51:03
%S 1,3,20,201,2688,44815,894528,20792205,551518208,16438822587,
%T 543934387200,19783668211153,784536321392640,33689132092480839,
%U 1557397919735103488,77117362592836807125,4072280214605427376128,228441851811771488284915,13566762607790788699226112,850372121882700252639269337
%N a(n) = n! * [x^n] exp(n*x)/(1 - 2*x).
%C The n-th term of the n-th binomial transform of A000165.
%H Robert Israel, <a href="/A295100/b295100.txt">Table of n, a(n) for n = 0..375</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F a(n) ~ 2^n * exp(n/2) * n!. - _Vaclav Kotesovec_, Nov 14 2017
%F a(n) = n! * Sum_{k=0..n} n^k*2^(n-k)/k! = 2^n*Gamma(n+1, n/2)*exp(n/2). - _Robert Israel_, Nov 14 2017
%p S:= series(exp(n*x)/(1-2*x),x,51):
%p seq(n!*coeff(S,x,n),n=0..50); # _Robert Israel_, Nov 14 2017
%t Table[n! SeriesCoefficient[Exp[n x]/(1 - 2 x), {x, 0, n}], {n, 0, 19}]
%Y Cf. A000165, A010844, A063170, A082032, A295098, A295099.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Nov 14 2017
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