OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..249
FORMULA
Given e.g.f. A(x) = Sum_{n>=0} a(n) * x^(2*n) / (2*n)!, then 0 = 1 + 2*A'^2 - A*A''.
Given e.g.f. A(x), then A'(x) / A(x) = B(x) where B() is the e.g.f. for A242240.
Given e.g.f. A(x), 1 / A(x) = A(-x).
EXAMPLE
G.f. = 1 + x + 3*x^2 + 27*x^3 + 441*x^4 + 11529*x^5 + 442827*x^6 + ...
E.g.f. = 1 + 1*x^2/2! + 3*x^4/4! + 27*x^6/6! + 441*x^8/8! + 11529*x^10/10! + ...
MATHEMATICA
a[ n_] := If[ n < 0, 0, With[{m = 2 n}, m! SeriesCoefficient[ Exp[ Integrate[ JacobiSN[x, 1/2] / JacobiCD[x, 1/2], x]], {x, 0, m}]]];
a:= With[{nmax = 110}, CoefficientList[Series[Exp[Integrate[JacobiSN[x, 1/2]/JacobiCD[x, 1/2], x]], {x, 0, nmax}], x]*Range[0, nmax]!][[1 ;; ;; 2]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 29 2018 *)
PROG
(PARI) {a(n) = my(m); if( n<0, 0, m = 2*n; m! * polcoeff( exp( intformal( serreverse( intformal( (1 + x^4 + x * O(x^m))^(-1/2))))), m))};
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, May 05 2017
STATUS
approved