%I A157316
%S A157316 2,168,6710208,80421395017344,268650181814894062310400,
%T A157316 241677817414364648836194235222953984,
%U A157316 57560679870262286682598360350282651217048664506368
%N A157316 G.f.: A(x) = tanh( Sum_{n>=0} 2^((2n+1)^2) * x^(2n+1)/(2n+1) ), with 
               zero terms omitted.
%C A157316 Compare g.f. to the expansion of the inverse tanh of x:
%C A157316 atanh(x) = log((1+x)/(1-x))/2 = x + x^3/3 + x^5/5 + x^7/7 +...
%e A157316 G.f.: A(x) = 2*x + 168*x^3 + 6710208*x^5 + 80421395017344*x^7 +...
%e A157316 atanh(A(x)) = 2*x + 2^9*x^3/3 + 2^25*x^5/5 + 2^49/7*x^7 +...
%o A157316 (PARI) {a(n)=polcoeff(tanh(sum(m=0,n,2^((2*m+1)^2)*x^(2*m+1)/(2*m+1))+O(x^(2*n+2))),
               2*n+1)}
%Y A157316 Cf. A157315.
%Y A157316 Sequence in context: A139928 A142602 A005020 this_sequence A163970 A007760 
               A051030
%Y A157316 Adjacent sequences: A157313 A157314 A157315 this_sequence A157317 A157318 
               A157319
%K A157316 nonn
%O A157316 0,1
%A A157316 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 19 2009