OFFSET
0,3
COMMENTS
A variant of A023881, which is defined by g.f.:
exp( Sum_{n>=1} [Sum_{d|n} d^n] * x^n/n )
where A023881 is the number of partitions in expanding space.
Compare also to the g.f. of A006950 given by:
exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d] * x^n/n ),
where A006950(n) is the number of partitions of n in which each even part occurs with even multiplicity.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..380
FORMULA
a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - Vaclav Kotesovec, Aug 17 2015
EXAMPLE
G.f.: 1 + x + 2*x^2 + 11*x^3 + 79*x^4 + 713*x^5 + 8486*x^6 +...
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, (-1)^(m-d)*d^m)*x^m/m)+x*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 22 2009
STATUS
approved