A068113 Numerator of coefficient of (-x^2)^n in F(x)*F(-x) where F(x) = Sum_{k>=0} x^k/(k!)^3.

1, 3, 5, 7, 11, 143, 221, 323, 7429, 437, 667, 20677, 899, 33263, 1363783, 2022161, 3065857, 3065857, 162490421, 4391633, 259106347, 385499687, 8965109, 600662303, 907383479, 66238993967, 66238993967, 98733594781, 8194888366823

Offset

0,2

References

Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Hypergeometric series, p. 62.

G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 7.

Links

Table of n, a(n) for n=0..28.

Formula

F(x)*F(-x) = Sum_{n>=0} ((3*n)!/(n!*(2*n)!)^3)*(-x^2)^n.

a(n) = numerator((3*n)!/(n!*(2*n)!)^3) (see Hardy). - Stefano Spezia, Apr 26 2025

Mathematica

F[x_] := HypergeometricPFQ[{}, {1, 1}, x]; F[x]*F[-x] + O[x]^58 // CoefficientList[#, x^2]& // Numerator // Abs (* Jean-François Alcover, Nov 17 2016 *)
a[n_]:=Numerator[(3n)!/(n!(2n)!)^3]; Array[a, 29, 0] (* Stefano Spezia, Apr 26 2025 *)

Crossrefs

Cf. A068112.

Sequence in context: A083840 A088051 A159471 * A068831 A109862 A069804

Adjacent sequences: A068110 A068111 A068112 * A068114 A068115 A068116

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Mar 21 2002

Status

approved