OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
F. Chapoton, F. Hivert, J.-C. Novelli, A set-operad of formal fractions and dendriform-like sub-operads, arXiv preprint arXiv:1307.0092 [math.CO], 2013.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 861
B. R. Jones, On tree hook length formulas, Feynman rules and B-series, Master's thesis, Simon Fraser University, 2014.
FORMULA
E.g.f.: B(exp(x)-1) where B is e.g.f. of A000169.
E.g.f.: Series_Reversion( log(1 + x*exp(-x)) ). - Paul D. Hanna, Jan 24 2016
a(n) = Sum_{k=1..n} Stirling2(n, k)*k^(k-1). - Vladeta Jovovic, Sep 17 2003
Stirling transform of A000169. - Michael Somos, Jun 09 2012
a(n) ~ sqrt(1+exp(1)) * n^(n-1) / (exp(n) * (log(1+exp(-1)))^(n-1/2)). - Vaclav Kotesovec, Feb 17 2014
EXAMPLE
G.f. = x + 3*x^2 + 16*x^3 + 133*x^4 + 1521*x^5 + 22184*x^6 + 393681*x^7 + ...
MATHEMATICA
nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[ ComposeSeries[ Series[t, {x, 0, nn}], Series[Exp[x]-1 , {x, 0, nn}]], x] (* Geoffrey Critzer, Sep 16 2012 *)
PROG
(PARI) {a(n) = sum( k=1, n, stirling(n, k, 2) * k^(k - 1))}; /* Michael Somos, Jun 09 2012 */
(PARI) {a(n) = n! * polcoeff( serreverse( log(1 + x*exp(-x +x*O(x^n))) ), n)}
for(n=1, 30, print1(a(n), ", ")) \\ Paul D. Hanna, Jan 24 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Mar 15 1999
STATUS
approved