A157316 G.f.: A(x) = tanh( Sum_{n>=0} 2^((2n+1)^2) * x^(2n+1)/(2n+1) ), with zero terms omitted.

2, 168, 6710208, 80421395017344, 268650181814894062310400, 241677817414364648836194235222953984, 57560679870262286682598360350282651217048664506368

Offset

0,1

Comments

Compare g.f. to the expansion of the inverse tanh of x:

arctanh(x) = log((1+x)/(1-x))/2 = x + x^3/3 + x^5/5 + x^7/7 + ...

Links

Table of n, a(n) for n=0..6.

Example

G.f.: A(x) = 2*x + 168*x^3 + 6710208*x^5 + 80421395017344*x^7 + ...
arctanh(A(x)) = 2*x + 2^9*x^3/3 + 2^25*x^5/5 + 2^49/7*x^7 + ...

Prog

(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)}

Crossrefs

Cf. A157315.

Sequence in context: A142602 A200042 A005020 * A007760 A230511 A209607

Adjacent sequences: A157313 A157314 A157315 * A157317 A157318 A157319

Keyword

nonn

Author

Paul D. Hanna, Mar 19 2009

Status

approved