Search: id:A052882
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%I A052882
%S A052882 0,1,2,9,52,375,3246,32781,378344,4912515,70872610,1124723193,
%T A052882 19471590876,365190378735,7376016877334,159620144556645,
%U A052882 3684531055645648,90366129593683035,2346673806524446218
%N A052882 A simple grammar: rooted ordered set partitions.
%C A052882 Recurrence (see Mathematica line) is similar to that for Genocchi numbers 
               A001469 - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 09 
               2001
%C A052882 Stirling transform of A024167(n)=[1,1,5,14,94,...] is a(n)=[1,2,9,52,
               375,...]. - Michael Somos Mar 04 2004
%C A052882 Stirling transform of a(n)=[0,2,9,52,375,...] is A087301(n+1)=[0,2,3,
               20,...]. - Michael Somos Mar 04 2004
%H A052882 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=855">
               Encyclopedia of Combinatorial Structures 855</a>
%H A052882 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/NoteBooks/
               NoteBook2/chapterII/page10.htm">Notebook entry</a>
%F A052882 E.g.f.: x/(2-exp(x)).
%F A052882 a(n) = (1/2)*sum(k=0, n-1, B_k*A000629(k)*binomial(n, k)) where B_k is 
               the k-th Bernoulli number. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 19 2005
%p A052882 spec := [S,{C=Sequence(B),B=Set(Z,1 <= card),S=Prod(Z,C)},labeled]: seq(combstruct[count](spec,
               size=n), n=0..20);
%p A052882 with(combinat):a:=n->sum(sum(sum((-1)^(k-i)*binomial(k, i)*i^n, i=0..n),
               k=0..n),m=0..n): seq(a(n), n=-1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 03 2007
%t A052882 a[1] := 1; a[n_] := a[n]=Sum[ Binomial[n, m] a[ n-m], {m, 1, n-1}]
%o A052882 (PARI) a(n)=if(n<0,0,n!*polcoeff(subst(x/(1-y),y,exp(x+x*O(x^n))-1),n))
%Y A052882 Cf. A001469.
%Y A052882 For n>0, a(n)=n*A000670(n).
%Y A052882 Sequence in context: A069271 A006152 A143508 this_sequence A143922 A110322 
               A161631
%Y A052882 Adjacent sequences: A052879 A052880 A052881 this_sequence A052883 A052884 
               A052885
%K A052882 easy,nonn
%O A052882 0,3
%A A052882 encyclopedia(AT)pommard.inria.fr, Jan 25 2000

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