%I A052841
%S A052841 1,0,2,6,38,270,2342,23646,272918,3543630,51123782,811316286,
%T A052841 14045783798,263429174190,5320671485222,115141595488926,
%U A052841 2657827340990678,65185383514567950,1692767331628422662
%N A052841 A simple grammar.
%C A052841 Stirling transform of A005359(n)=[0,2,0,24,0,720,...] is a(n)=[0,2,6,
               38,270,...]. - Michael Somos Mar 04 2004
%C A052841 Stirling transform of -(-1)^n*A052657(n-1)=[0,0,2,-6,48,-240,...] is 
               a(n-1)=[0,0,2,6,38,270,...]. - Michael Somos Mar 04 2004
%C A052841 Stirling transform of -(-1)^n*A052558(n-1)=[1,-1,4,-12,72,-360,...] is 
               a(n-1)=[1,0,2,6,38,270,...]. - Michael Somos Mar 04 2004
%C A052841 Stirling transform of 2*A052591(n)=[2,4,24,96,...] is a(n+1)=[2,6,38,
               270,...]. - Michael Somos Mar 04 2004
%H A052841 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=808">
               Encyclopedia of Combinatorial Structures 808</a>
%H A052841 C. G. Bower, <a href="transforms2.html">Transforms (2)</a>
%F A052841 a( n) = (A000670(n) + (-1)^n)/2 = Sum_{k>=0} (k-1)^n/2^(k+1). - Vladeta 
               Jovovic (vladeta(AT)eunet.rs), Feb 02 2003
%F A052841 Also, a(n) = Sum[k=0..[n/2], (2k)!*Stirling2(n, 2k)]. - R. Stephan, May 
               23 2004
%F A052841 E.g.f.: 1/(exp(x)*(2-exp(x))).
%p A052841 spec := [S,{B=Prod(C,C),C=Set(Z,1 <= card),S=Sequence(B)},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%o A052841 (PARI) a(n)=if(n<0,0,n!*polcoeff(subst(1/(1-y^2),y,exp(x+x*O(x^n))-1),
               n))
%Y A052841 Inverse binomial transform of A000670.
%Y A052841 Sequence in context: A027322 A085447 A078673 this_sequence A068184 A067106 
               A032111
%Y A052841 Adjacent sequences: A052838 A052839 A052840 this_sequence A052842 A052843 
               A052844
%K A052841 easy,nonn
%O A052841 0,3
%A A052841 encyclopedia(AT)pommard.inria.fr, Jan 25 2000