cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

2, 168, 6710208, 80421395017344, 268650181814894062310400, 241677817414364648836194235222953984, 57560679870262286682598360350282651217048664506368
Offset: 0

Views

Author

Paul D. Hanna, Mar 19 2009

Keywords

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 + ...

Examples

			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 + ...
		

Crossrefs

Cf. A157315.

Programs

  • 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)}
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