A163572 G.f.: A(x) = exp( Sum_{n>=1} (1 + 2*A006519(n)*x)^n * x^n/n ) where A006519(n) is the highest power of 2 dividing n.
1, 1, 3, 7, 19, 39, 169, 765, 2183, 4131, 11561, 55157, 666381, 8175433, 68536455, 355280675, 1048740623, 1931107235, 5055100985, 13108206741, 38734589993, 143320957605, 1022112572635, 26523801989399, 914332703582521
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 39*x^5 + 169*x^6 +... log(A(x)) = (1+2*x)*x + (1+4*x)^2*x^2/2 + (1+2*x)^3*x^3/3 + (1+8*x)^4*x^4/4 +...
Programs
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PARI
{a(n)=polcoeff(exp(sum(m=1, n+1, (1+2^valuation(2*m,2)*x+x*O(x^n))^m*x^m/m)), n)}