A162416 - OEIS

%I #2 Mar 30 2012 18:37:17

%S 1,1,1,6,12,19,48,147,305,628,1607,3748,8140,18779,44521,102625,

%T 233230,540343,1254459,2877651,6614799,15288779,35283125,81210949,

%U 187173219,431917054,995565240,2293851990,5288703013,12194473395,28108088241

%N G.f.: A(x) = exp( Sum_{n>=1} A162415(n)^2*x^n/n ) where A162415 is defined by: Sum_{n>=0} x^(2^n-1) = exp( Sum_{n>=1} A162415(n)*x^n/n ).

%e G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 +...

%e log(A(x)) = x + x^2/2 + 4^2*x^3/3 + 5^2*x^4/4 + 6^2*x^5/5 + 10^2*x^6/6 +...

%e where the coefficients are the squares of the coefficients in L(x):

%e L(x) = log(1 + x + x^3 + x^7 + x^15 +...+ x^(2^n-1) +...);

%e L(x) = x - x^2/2 + 4*x^3/3 - 5*x^4/4 + 6*x^5/5 - 10*x^6/6 + 22*x^7/7 -+...

%o (PARI) {a(n)=local(L=Vec(log(sum(m=0,#binary(n),x^(2^m-1))+x*O(x^n)))); polcoeff(exp(sum(k=1,n,L[k]^2*k*x^k)+x*O(x^n)),n)}

%Y Cf. A162415.

%K nonn

%O 0,4

%A _Paul D. Hanna_, Jul 02 2009