cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A163203 #7 Aug 17 2015 06:17:37
%S A163203 1,1,2,11,79,713,8486,127372,2248390,45527161,1048442107,27060812167,
%T A163203 771886991408,24110090108332,818871809076474,30044771201925569,
%U A163203 1184069354974499199,49884064948928968400,2237283630465903060711
%N A163203 G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d^n] * x^n/n ).
%C A163203 A variant of A023881, which is defined by g.f.:
%C A163203 exp( Sum_{n>=1} [Sum_{d|n} d^n] * x^n/n )
%C A163203 where A023881 is the number of partitions in expanding space.
%C A163203 Compare also to the g.f. of A006950 given by:
%C A163203 exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d] * x^n/n ),
%C A163203 where A006950(n) is the number of partitions of n in which each even part occurs with even multiplicity.
%H A163203 Vaclav Kotesovec, <a href="/A163203/b163203.txt">Table of n, a(n) for n = 0..380</a>
%F A163203 a(n) ~ n^(n-1) * (1 + exp(-1)/n + (3*exp(-1)/2 + 2*exp(-2))/n^2). - _Vaclav Kotesovec_, Aug 17 2015
%e A163203 G.f.: 1 + x + 2*x^2 + 11*x^3 + 79*x^4 + 713*x^5 + 8486*x^6 +...
%o A163203 (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 A163203 Cf. A023881, A006950, A002129.
%K A163203 nonn
%O A163203 0,3
%A A163203 _Paul D. Hanna_, Jul 22 2009