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 A052875 A simple grammar. 6

%I

%S 0,0,2,12,74,540,4682,47292,545834,7087260,102247562,1622632572,

%T 28091567594,526858348380,10641342970442,230283190977852,

%U 5315654681981354,130370767029135900,3385534663256845322

%N A simple grammar.

%C Stirling transform of A005359(n-1)=[0,0,2,0,24,0,...] is a(n-1)=[0,0,2,12,74,...]. - Michael Somos Mar 04 2004

%C Stirling transform of -(-1)^n*A052566(n-1)=[1,-1,4,-6,48,...] is a(n-1)=[1,0,2,12,74,...]. - Michael Somos Mar 04 2004

%C Stirling transform of A000142(n)=[0,2,6,24,120,...] is a(n)=[0,2,12,74,...]. - Michael Somos Mar 04 2004

%C Stirling transform of A007680(n)=[2,10,42,216,...] is a(n+1)=[2,12,74,...]. - Michael Somos Mar 04 2004

%H INRIA Algorithms Project, <a href="http://algo.inria.fr/ecs/ecs?searchType=1&amp;service=Search&amp;searchTerms=846">Encyclopedia of Combinatorial Structures 846</a>

%F Second column of A084416: Sum_{i=2..n} i!*Stirling2(n, i) = A000670(n)-1. - _Vladeta Jovovic_, Sep 15 2003

%F E.g.f.: (exp(x)-1)^2/(2-exp(x)).

%p spec := [S,{B=Set(Z,1 <= card),C=Sequence(B,1 <= card),S=Prod(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%o (PARI) a(n)=if(n<0,0,n!*polcoeff(subst(y^2/(1-y),y,exp(x+x*O(x^n))-1),n))

%K easy,nonn

%O 0,3

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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