A191415 E.g.f. A(x) satisfies A(x) = x*(1 - A(x))^(-A(x)).

1, 0, 6, 12, 340, 2340, 58338, 786240, 20890224, 428954400, 12845444040, 351885980160, 12049309321608, 408370359196800, 15960347878230000, 639599649237319680, 28303809398414031360, 1302999243310662912000, 64651744760744124697536, 3352722890027561625600000

Offset: 1

Author

Vladimir Kruchinin, Jun 01 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..380

Programs

Mathematica

Flatten[{1,Table[n!*Sum[(n^(k-1)*(-1)^(n-2*k-1)*StirlingS1[n-k-1,k])/(n-k-1)!,{k,1,n-1}],{n,2,20}]}]  (* Vaclav Kotesovec, Aug 10 2014 after Vladimir Kruchinin *)

Maxima

a(n):=if n=1 then 1 else (n!*sum((n^(k-1)*(-1)^(n-2*k-1)*stirling1(n-k-1,k))/(n-k-1)!,k,1,n-1));

PARI

a(n) = if (n==1, 1, n!*sum(k=1, n-1, (n^(k-1)*(-1)^(n-2*k-1)*stirling(n-k-1, k, 1))/(n-k-1)!)); \\ Michel Marcus, Oct 13 2017

Formula

a(n) = n!*Sum_{k=1..n-1} (n^(k-1)*(-1)^(n-2*k-1)*Stirling1(n-k-1, k))/(n-k-1)!, n > 1, a(1)=1.

a(n) ~ n^(n-1) / (sqrt(1-(2-s)*(1-s)*s) * exp(n) * s^(n-1) * (1-s)^(s*n-1)), where s = 0.530402312512063468084914246777198746... is the root of the equation (1-s)*(2 + s + s*log(1-s)) = 1. - Vaclav Kotesovec, Aug 10 2014