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 A163203 G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d^n] * x^n/n ). 2

%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_{d|n} (-1)^(n-d)*d^n] * x^n/n ).

%C A variant of A023881, which is defined by g.f.:

%C exp( Sum_{n>=1} [Sum_{d|n} 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_{d|n} (-1)^(n-d)*d] * x^n/n ),

%C where A006950(n) is the number of partitions of n in which each even part occurs with even multiplicity.

%H Vaclav Kotesovec, <a href="/A163203/b163203.txt">Table of n, a(n) for n = 0..380</a>

%F a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - _Vaclav Kotesovec_, Aug 17 2015

%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)^(m-d)*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

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