A309206 a(n) = (2*n)!/A309205(n).

1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 1, 1, 13, 19, 5, 1, 221, 1, 1, 1, 1, 1, 13, 17, 5, 1, 47, 4913, 29, 7, 11, 53, 1, 47, 325, 13, 1147, 41, 1, 1, 41, 1081, 11, 1, 5, 1, 1, 83, 1, 1, 133, 1, 2491, 97, 5, 103, 61, 1, 1, 19, 226493, 1, 1, 1, 5, 31, 1, 1, 1, 1271, 289

Offset: 0

Author

N. J. A. Sloane, Jul 28 2019, following a suggestion from Bill Gosper

Keywords

• nonn
• frac

Comments

Bill Gosper points out that this is a better fingerprint for the series than A309205.

Crossrefs

Cf. A309204, A309205.

Programs

Mathematica

F[n_] := Module[{p}, p = 1 + O[x]; For[k=2, k <= n, k++, p = Cos[x p]]; p];
seq[n_] := Module[{v}, v = CoefficientList[F[n], x]; Table[(2(k - 1))!/ Denominator[v[[2k - 1]]], {k, 1, n}]];
seq[71] (* Jean-François Alcover, Aug 27 2019, from PARI *)

PARI

\\ here F(n) gives n terms of power series.
F(n)={my(p=1+O(x)); for(k=2, n, p=cos(x*p)); p}
seq(n)={my(v=Vec(F(n))); vector(n, k, (2*(k-1))!/denominator(v[2*k-1]))} \\ Andrew Howroyd, Aug 17 2019

Extensions

Terms a(31) and beyond from Andrew Howroyd, Aug 17 2019