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%I #7 Oct 01 2015 12:41:23
%S 1,2,14,202,16858,6746346,11466918526,80444425726274,
%T 2306004013900856642,268654794950929597256002,
%U 126765597355485476411443388062,241678070949320865028012988979962410,1858395916568294857820278937430319959202010,57560683587057503330693629888859064500206488317834
%N G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^(d^2) * n^2/d^2 ).
%C a(n) == 2 (mod 4) for n>0.
%e G.f.: A(x) = 1 + 2*x + 14*x^2 + 202*x^3 + 16858*x^4 + 6746346*x^5 +...
%e The logarithm of the g.f. begins:
%e log(A(x)) = 2*x + 24*x^2/2 + 530*x^3/3 + 65632*x^4/4 + 33554482*x^5/5 + 68719479000*x^6/6 + 562949953421410*x^7/7 + 18446744073709814144*x^8/8 +...+ A262009(n)*x^n/n +...
%e where
%e A262009(n) = Sum_{d|n} 2^(d^2) * n^2/d^2.
%o (PARI) {a(n) = polcoeff( exp(sum(m=1,n,x^m/m * sumdiv(m,d, 2^(d^2) * m^2/d^2))+x*O(x^n)),n)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A262009 (log).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 01 2015
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