A225697 Numerators of mass formula for vacuum graphs for a phi^4 field theory.

1, 1, 35, 385, 25025, 1616615, 260275015, 929553625, 835668708875, 321732452916875, 30950661970603375, 4960547004924886375, 1165728546157348298125, 74696298380697779410625, 31105672825676289568853125, 6973891847516624121336870625, 2977851818889598499810843756875

Offset

0,3

Links

Table of n, a(n) for n=0..16.

C. M. Bender and K. A. Milton, Continued fraction as a discrete nonlinear transform, arXiv:hep-th/9304052, 1993. See V_n with N=2.

Example

1, 1/8, 35/384, 385/3072, 25025/98304, 1616615/2359296, 260275015/113246208,
929553625/100663296, 835668708875/19327352832, 321732452916875/1391569403904,
30950661970603375/22265110462464, 4960547004924886375/534362651099136, ...

Mathematica

V[n_] := (4 n - 1)!!/(4!^n n!);
Table[V[n] // Numerator, {n, 0, 16}] (* Jean-François Alcover, Sep 05 2018 *)

Crossrefs

Cf. A225698.

Sequence in context: A027803 A267749 A073567 * A133458 A238539 A075664

Adjacent sequences: A225694 A225695 A225696 * A225698 A225699 A225700

Keyword

nonn,frac

Author

N. J. A. Sloane, May 30 2013

Status

approved