A163203 G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d^n] * x^n/n ).

1, 1, 2, 11, 79, 713, 8486, 127372, 2248390, 45527161, 1048442107, 27060812167, 771886991408, 24110090108332, 818871809076474, 30044771201925569, 1184069354974499199, 49884064948928968400, 2237283630465903060711

Offset: 0

Author

Paul D. Hanna, Jul 22 2009

Keywords

• nonn

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.

Examples

			G.f.: 1 + x + 2*x^2 + 11*x^3 + 79*x^4 + 713*x^5 + 8486*x^6 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..380

Crossrefs

Cf. A023881, A006950, A002129.

Programs

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)}

Formula

a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - Vaclav Kotesovec, Aug 17 2015