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%I #8 Oct 14 2014 08:29:55
%S 1,3,17,285,21747,7894143,12593691755,84961748935779,
%T 2379148487805445513,273416748863491468927893,
%U 128009274688933686165252807225,242979449433397149030644307317592609,1863847996727745781866688849374488247858333,57652096246331953203644653244501049018464175026133
%N G.f.: A(x) = exp( Sum_{n>=1} (2^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
%C More generally, it appears that for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.
%F Equals row sums of triangle A155810.
%F a(n) = (1/n)*Sum_{k=1..n} (2^k + 1)^k * a(n-k) for n>0, with a(0)=1.
%F a(n) = B_n( 0!*(2^1+1)^1, 1!*(2^2+1)^2, 2!*(2^3+1)^3, ..., (n-1)!*(2^n+1)^n ) / n!, where B_n() is the n-th complete Bell polynomial. - _Max Alekseyev_, Oct 10 2014
%e G.f.: A(x) = 1 + 3*x + 17*x^2 + 285*x^3 + 21747*x^4 + 7894143*x^5 +...
%e log(A(x)) = 3*x + 5^2*x^2/2 + 9^3*x^3/3 + 17^4*x^4/4 + 33^5*x^5/5 +...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1,n+1,(2^m+1)^m*x^m/m)+x*O(x^n)),n)}
%Y Cf. A155200, A155202, A155810 (triangle), variants: A155204, A155208.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 04 2009
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