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%I A165940 #2 Mar 30 2012 18:37:18
%S A165940 1,2,10,152,7684,1352096,852120928,1960591940480,16697154282192928,
%T A165940 531801639623740649984,63854080509077223292639744,
%U A165940 29089348119991257994736112048128
%N A165940 G.f.: Sum_{n>=0} a(n)*x^n/2^(n^2+n) = exp( Sum_{n>=1} x^n/[n*2^(n^2)] ).
%C A165940 Conjectured to consist entirely of integers.
%e A165940 G.f.: 1 + 2*x/2^2 + 10*x^2/2^6 + 152*x^3/2^12 + 7684*x^4/2^20 +...
%e A165940 = exp( x/2 + x^2/(2*2^4) + x^3/(3*2^9) + x^4/(4*2^16) +... ).
%e A165940 Evaluated at x=1:
%e A165940 Sum_{n>=0} a(n)/2^(n^2+n) = 1.7021716250154556344906565654972646...
%o A165940 (PARI) {a(n)=2^(n^2+n)*polcoeff(exp(sum(m=1, n+1, 2^(-m^2)*x^m/m)+x*O(x^n)), n)}
%Y A165940 Cf. A155200.
%K A165940 nonn
%O A165940 0,2
%A A165940 _Paul D. Hanna_, Oct 01 2009

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