%I
%S 1,1,2,11,79,713,8486,127372,2248390,45527161,1048442107,27060812167,
%T 771886991408,24110090108332,818871809076474,30044771201925569,
%U 1184069354974499199,49884064948928968400,2237283630465903060711
%N G.f.: exp( Sum_{n>=1} [Sum_{dn} (1)^(nd)*d^n] * x^n/n ).
%C A variant of A023881, which is defined by g.f.:
%C exp( Sum_{n>=1} [Sum_{dn} d^n] * x^n/n )
%C where A023881 is the number of partitions in expanding space.
%C Compare also to the g.f. of A006950 given by:
%C exp( Sum_{n>=1} [Sum_{dn} (1)^(nd)*d] * x^n/n ),
%C where A006950(n) is the number of partitions of n in which each even part occurs with even multiplicity.
%e G.f.: 1 + x + 2*x^2 + 11*x^3 + 79*x^4 + 713*x^5 + 8486*x^6 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, (1)^(md)*d^m)*x^m/m)+x*O(x^n)), n)}
%Y Cf. A023881, A006950, A002129.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 22 2009
