A275052 G.f.: 3F2([1/7, 2/7, 4/7], [1/2, 1], 2401 x).

1, 112, 103488, 139087872, 219932697600, 380982080962560, 699690909055057920, 1338362619711643975680, 2637829075787918298316800, 5319794376634771700187136000, 10925401705883689450455905075200, 22771065347191895949498972005990400, 48042740185717267168321727861725593600

Offset

0,2

Comments

"Other hypergeometric 'blind spots' for Christol’s conjecture" - (see Bostan link).

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..200

A. Bostan, S. Boukraa, G. Christol, S. Hassani, J-M. Maillard Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity, arXiv:1211.6031 [math-ph], 2012.

Formula

G.f.: hypergeom([1/7, 2/7, 4/7], [1/2, 1], 2401*x).

From Vaclav Kotesovec, Jul 28 2016: (Start)

Recurrence: n^2*(2*n - 1)*a(n) = 14*(7*n - 6)*(7*n - 5)*(7*n - 3)*a(n-1).

a(n) ~ sqrt(Pi) * 7^(4*n) / (Gamma(1/7) * Gamma(2/7) * Gamma(4/7) * n^(3/2)).

(End)

a(n) = 9604^n*Gamma(1/7+n)*Gamma(2/7+n)*Gamma(4/7+n)/(n!*(2n)!*Gamma(1/7)*Gamma(2/7)*Gamma(4/7)). - Benedict W. J. Irwin, Aug 05 2016

Example

1 + 112*x + 103488*x^2 + 139087872*x^3 + ...

Mathematica

CoefficientList[Series[HypergeometricPFQ[{1/7, 2/7, 4/7}, {1/2, 1}, 2401 x], {x, 0, 12}], x] (* Michael De Vlieger, Jul 26 2016 *)
a[n_] := FullSimplify[(9604^n Gamma[1/7 + n] Gamma[2/7 + n] Gamma[4/7 + n])/(n!(2n)! Gamma[1/7] Gamma[2/7] Gamma[4/7])] (* Benedict W. J. Irwin, Aug 05 2016 *)

Prog

(PARI) \\ system("wget http://www.jjj.de/pari/hypergeom.gpi");
read("hypergeom.gpi");
N = 12; x = 'x + O('x^N);
Vec(hypergeom([1/7, 2/7, 4/7], [1/2, 1], 2401*x, N))

Crossrefs

Cf. A268545-A268555.

Sequence in context: A270146 A184898 A270113 * A180039 A261949 A159432

Adjacent sequences: A275049 A275050 A275051 * A275053 A275054 A275055

Keyword

nonn

Author

Gheorghe Coserea, Jul 20 2016

Status

approved