A163572 - OEIS

%I #2 Mar 30 2012 18:37:18

%S 1,1,3,7,19,39,169,765,2183,4131,11561,55157,666381,8175433,68536455,

%T 355280675,1048740623,1931107235,5055100985,13108206741,38734589993,

%U 143320957605,1022112572635,26523801989399,914332703582521

%N 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.

%e G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 39*x^5 + 169*x^6 +...

%e 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 +...

%o (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)}

%Y Cf. A156100, A159308, A163189.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jul 31 2009