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 A163203 G.f.: exp( Sum_{n>=1} [Sum_{d|n} (-1)^(n-d)*d^n] * x^n/n ). 2
 1, 1, 2, 11, 79, 713, 8486, 127372, 2248390, 45527161, 1048442107, 27060812167, 771886991408, 24110090108332, 818871809076474, 30044771201925569, 1184069354974499199, 49884064948928968400, 2237283630465903060711 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A023881, A006950, A002129. Sequence in context: A151418 A154273 A253256 * A142722 A320095 A099661 Adjacent sequences: A163200 A163201 A163202 * A163204 A163205 A163206 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 22 2009 STATUS approved

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Last modified August 6 23:00 EDT 2024. Contains 375002 sequences. (Running on oeis4.)