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%I #7 May 12 2017 19:41:37
%S 1,2,32,512,262144,33554432,137438953472,562949953421312,
%T 147573952589676412928,2417851639229258349412352,
%U 2535301200456458802993406410752,2658455991569831745807614120560689152
%N Denominator in the coefficient of x^n in exp( Sum_{m>=1} x^m/(m*2^(m^2)) ).
%C It is surprising that these terms should consist only of powers of 2.
%F a(n) = 2^(n^2)*A006519(n) where A006519(n) = highest power of 2 dividing n [conjecture].
%e G(x) = exp( x/2 + x^2/(2*2^4) + x^3/(3*2^9) + x^4/(4*2^16) +...)
%e G(x) = 1 + 1/2*x + 5/32*x^2 + 19/512*x^3 + 1921/262144*x^4 +...
%t Table[Denominator@ SeriesCoefficient[Exp[Sum[x^m/(m*2^(m^2)), {m, 1, n}]], {x, 0, n}], {n, 0, 11}] (* _Michael De Vlieger_, May 12 2017 *)
%o (PARI) {a(n) = denominator(polcoeff(exp(sum(m=1, n+1, x^m/(m*2^(m^2))) + x*O(x^n)), n))}
%Y Cf. A174490 (numerators).
%K frac,nonn
%O 0,2
%A _Paul D. Hanna_, Mar 25 2010
%E Edited by _Paul D. Hanna_, Mar 29 2010