OFFSET
0,3
LINKS
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = n! * sum(k=0..n, (n+1)^(k-1)*abs(stirling1(n-k,k))/(n-k)!).
a(n) ~ s*(1-r*s) * n^(n-1) / (sqrt(1 - r*s*(2-r*s)*(1-r*s)) * exp(n) * r^n), where r = 0.35521237986941340511033292... and s = 1.49319771092171695325266171... are roots of the system of equations s = (1-r*s)^(-r*s), r*s*(r*s+(-1+r*s)*log(1-r*s)) = 1-r*s. - Vaclav Kotesovec, May 03 2015
E.g.f.: (1/x) * Series_Reversion( x*(1 - x)^x ). - Seiichi Manyama, Sep 21 2024
MAPLE
with(combinat):
a := n-> n! * add((n+1)^(k-1)*abs(stirling1(n-k, k))/(n-k)!, k=0..n):
seq(a(n), n=0..20);
MATHEMATICA
a[n_] := n! * Sum[(n+1)^(k-1)*Abs[StirlingS1[n-k, k]]/(n-k)!, {k, 0, n}]; Table [a[n], {n, 0, 20}] (* Jean-François Alcover, Apr 21 2015, from formula *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 03 2011
EXTENSIONS
Edited by Alois P. Heinz, Feb 03 2011
STATUS
approved