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A209902 E.g.f.: Product_{n>=1} 1/(1 - x^n)^(1/n!).

%I A209902 #6 Nov 03 2014 16:19:08
%S A209902 1,1,3,10,50,261,1877,13511,122663,1150988,12656562,142842855,
%T A209902 1882666887,24961232401,375233443223,5784328028680,98433762560780,
%U A209902 1704971188321787,32593405802749763,629093184347294419,13243913786996162915,283647771230983625422
%N A209902 E.g.f.: Product_{n>=1} 1/(1 - x^n)^(1/n!).
%H A209902 Vaclav Kotesovec, <a href="/A209902/b209902.txt">Table of n, a(n) for n = 0..300</a>
%F A209902 E.g.f.: exp( Sum_{n>=1} (exp(x^n) - 1)/n ).
%F A209902 E.g.f.: exp( Sum_{n>=1} A087906(n)*x^n/n! ) where A087906(n) = Sum_{d|n} (n-1)!/(d-1)!.
%F A209902 E.g.f.: Product_{n>=1} B(x^n)^(1/n) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.
%e A209902 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 50*x^4/4! + 261*x^5/5! +...
%e A209902 such that
%e A209902 A(x) = 1/((1-x) * (1-x^2)^(1/2) * (1-x^3)^(1/3!) * (1-x^4)^(1/4!) *...).
%o A209902 (PARI) {a(n)=n!*polcoeff(prod(m=1,n,1/(1-x^m+x*O(x^n))^(1/m!)),n)}
%o A209902 for(n=0,21,print1(a(n),", "))
%Y A209902 Cf. A087906.
%K A209902 nonn
%O A209902 0,3
%A A209902 _Paul D. Hanna_, Mar 14 2012