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E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(x).
8

%I #9 Nov 05 2016 21:05:52

%S 1,1,3,17,150,1869,30937,652147,16971392,532403448,19756591654,

%T 854013305595,42459118750496,2401987801594055,153207626004501247,

%U 10930853009024058261,866325783375527683256,75806831093269510084028

%N E.g.f. A(x) satisfies: A(1 - exp(-x)) = 1 + x*A(x).

%H G. C. Greubel, <a href="/A135750/b135750.txt">Table of n, a(n) for n = 0..250</a>

%F E.g.f. A(x) satisfies: A(x) = 1 - log(1-x)*A(-log(1-x)).

%F a(n) = Sum_{k=1..n} ( k*(-1)^(n-k)*stirling1(n,k)*a(k-1) ), n>0, a(0)=1. - _Vladimir Kruchinin_, Nov 28 2011

%t Clear[a]; a[0]:= 1; a[n_]:= a[n] = Sum[k*(-1)^(n - k)*StirlingS1[n, k]*a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 25}] (* _G. C. Greubel_, Nov 05 2016 *)

%o (PARI) {a(n)=local(A=1+x);for(i=0,n,A=1-log(1-x+x*O(x^n))* (subst(A,x,-log(1-x+x*O(x^n)))));n!*polcoeff(A,n)}

%o (Maxima)

%o a(n):=if n=0 then 1 else sum(k*(-1)^(n-k)*stirling1(n,k)*a(k-1),k,1,n); /* _Vladimir Kruchinin_, Nov 28 2011 */

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 27 2007