A052851 Expansion of e.g.f. 1/2 - (1/2)*(1+4*log(1-x))^(1/2).
0, 1, 3, 20, 220, 3424, 69008, 1706256, 49956240, 1689497376, 64799254752, 2778906776832, 131756614920192, 6843405231815424, 386414606189283072, 23567401521343170048, 1543994621969805135360, 108137637714495023354880, 8062825821198926369725440
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..360
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 819
- Index entries for reversions of series
Programs
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Maple
spec := [S,{B=Cycle(Z),S=Prod(B,C),C=Sequence(S)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); -
Mathematica
CoefficientList[Series[1/2-1/2*(1+4*Log[1-x])^(1/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 2013 *) -
Maxima
a(n):=sum(stirling1(n,k)*k!*binomial(2*k-2,k-1)/k*(-1)^(n+k), k,1,n); /* Vladimir Kruchinin, May 12 2012 */
Formula
E.g.f.: 1/2 - (1/2)*(1-4*log(-1/(-1+x)))^(1/2).
a(n) = Sum_{k=1..n} Stirling1(n,k)*k!*C(2*k-2,k-1)/k*(-1)^(n+k). - Vladimir Kruchinin, May 12 2012
a(n) ~ n^(n-1)/(sqrt(2)*exp(3*n/4)*(exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Sep 30 2013
From Seiichi Manyama, Sep 09 2024: (Start)
E.g.f. satisfies A(x) = (-log(1 - x)) / (1 - A(x)).
E.g.f.: Series_Reversion( 1 - exp(-x * (1 - x)) ). (End)
Extensions
New name using e.g.f., Vaclav Kotesovec, Sep 30 2013
Comments