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%I #31 May 20 2018 09:43:13
%S 1,2,6,18,64,220,888,3192,15104,48096,338400,285120,13728768,
%T -75484032,1327431168,-15621137280,232048220160,-3468200017920,
%U 56208508250112,-959557688285184,17344153658234880,-330228975428997120,6611419866845122560,-138844103855232061440
%N n-th derivative of x^(2*x) at x=1.
%H Robert Israel, <a href="/A265945/b265945.txt">Table of n, a(n) for n = 0..450</a>
%F E.g.f.: (x+1)^(2*x+2).
%F From _Robert Israel_, Dec 23 2015: (Start)
%F a(n) = Sum_{k=0..n} binomial(n,j)*A005727(j)*A005727(n-j).
%F a(n+1) = 2*(a(n) + Sum_{k=0..n-1} (-1)^(n-1-k)*n!*a(k)/((n-k)*k!). (End)
%p S:= series((x+1)^(2*x+2), x, 51):
%p seq(coeff(S,x,j)*j!, j=0..50); # _Robert Israel_, Dec 23 2015
%t With[{nn=30},CoefficientList[Series[(x+1)^(2x+2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 20 2018 *)
%Y Cf. A005727.
%K sign
%O 0,2
%A _Ben Paul Thurston_, Dec 23 2015
%E More terms from _Alois P. Heinz_, Dec 23 2015
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