A262008 G.f.: exp( Sum_{n>=1} x^n/n * Sum_{d|n} 2^(d^2) * n^2/d^2 ).
1, 2, 14, 202, 16858, 6746346, 11466918526, 80444425726274, 2306004013900856642, 268654794950929597256002, 126765597355485476411443388062, 241678070949320865028012988979962410, 1858395916568294857820278937430319959202010, 57560683587057503330693629888859064500206488317834
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + 2*x + 14*x^2 + 202*x^3 + 16858*x^4 + 6746346*x^5 +...
The logarithm of the g.f. begins:
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 +...
where
A262009(n) = Sum_{d|n} 2^(d^2) * n^2/d^2.
Crossrefs
Cf. A262009 (log).
Programs
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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)} for(n=0,20,print1(a(n),", "))
Comments