cp's OEIS Frontend

A157314 G.f.: A(x) = exp( Sum_{n>=1} A157313(n)*x^n/n ) = 1/Product_{n>=1} (1 - A157313(n-1)*x^n).

%I A157314 #3 Mar 30 2012 18:37:16
%S A157314 1,1,2,5,16,62,298,1700,11448,88622,778532,7636888,82782697,981775224,
%T A157314 12643542295,175638751080,2617558335383,41650633309937,
%U A157314 704712768652527,12632584581030449,239150363847113653,4767657035201958150
%N A157314 G.f.: A(x) = exp( Sum_{n>=1} A157313(n)*x^n/n ) = 1/Product_{n>=1} (1 - A157313(n-1)*x^n).
%e A157314 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 62*x^5 + 298*x^6 +...
%e A157314 where the exponential:
%e A157314 A(x) = exp(x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 216*x^5/5 + 1326*x^6/6 +...)
%e A157314 and the product:
%e A157314 1/A(x) = (1 - x)(1 - x^2)(1 - 3*x^3)(1 - 10*x^4)(1 - 43*x^5)(1 - 216*x^6)*...
%e A157314 generate A(x) using the same coefficients (after initial term):
%e A157314 A157313=[1,1,3,10,43,216,1326,9283,74667,672085,6730098,74031079,...].
%Y A157314 Cf. A157313, A157312.
%K A157314 nonn
%O A157314 0,3
%A A157314 _Paul D. Hanna_, Mar 10 2009