A162416 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 ).

1, 1, 1, 6, 12, 19, 48, 147, 305, 628, 1607, 3748, 8140, 18779, 44521, 102625, 233230, 540343, 1254459, 2877651, 6614799, 15288779, 35283125, 81210949, 187173219, 431917054, 995565240, 2293851990, 5288703013, 12194473395, 28108088241

Offset: 0

Author

Paul D. Hanna, Jul 02 2009

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 +...
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 +...
where the coefficients are the squares of the coefficients in L(x):
L(x) = log(1 + x + x^3 + x^7 + x^15 +...+ x^(2^n-1) +...);
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 -+...
		

Crossrefs

Cf. A162415.

Programs

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)}