0,3

Recurrence (see Mathematica line) is similar to that for Genocchi numbers A001469 - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jan 09 2001

Stirling transform of A024167(n)=[1,1,5,14,94,...] is a(n)=[1,2,9,52,375,...]. - Michael Somos Mar 04 2004

Stirling transform of a(n)=[0,2,9,52,375,...] is A087301(n+1)=[0,2,3,20,...]. - Michael Somos Mar 04 2004

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 855

S. Ramanujan, Notebook entry

E.g.f.: x/(2-exp(x)).

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

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

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

a[1] := 1; a[n_] := a[n]=Sum[ Binomial[n, m] a[ n-m], {m, 1, n-1}]

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

Cf. A001469.

For n>0, a(n)=n*A000670(n).

Sequence in context: A069271 A006152 A143508 this_sequence A143922 A110322 A161631

Adjacent sequences: A052879 A052880 A052881 this_sequence A052883 A052884 A052885

easy,nonn

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