A184949 E.g.f. satisfies A(x) = (1-x*A(x))^(-x*A(x)).
1, 0, 2, 3, 68, 390, 8334, 98280, 2321136, 42895440, 1167767640, 29323831680, 926869947816, 29169311371200, 1064023191882000, 39974978077332480, 1664929964612590080, 72388846850592384000, 3402723408460217089344, 167636144501378081280000, 8796533195129444799189120
Offset: 0
Keywords
Links
- Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
- Index entries for reversions of series
Crossrefs
Cf. A371147.
Programs
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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);
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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 *)
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
Extensions
Edited by Alois P. Heinz, Feb 03 2011