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Numerators of mass formula for vacuum graphs for a phi^4 field theory.
7

%I #12 Sep 05 2018 10:34:55

%S 1,1,35,385,25025,1616615,260275015,929553625,835668708875,

%T 321732452916875,30950661970603375,4960547004924886375,

%U 1165728546157348298125,74696298380697779410625,31105672825676289568853125,6973891847516624121336870625,2977851818889598499810843756875

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

%H C. M. Bender and K. A. Milton, <a href="http://arxiv.org/abs/hep-th/9304052">Continued fraction as a discrete nonlinear transform</a>, arXiv:hep-th/9304052, 1993. See V_n with N=2.

%e 1, 1/8, 35/384, 385/3072, 25025/98304, 1616615/2359296, 260275015/113246208,

%e 929553625/100663296, 835668708875/19327352832, 321732452916875/1391569403904,

%e 30950661970603375/22265110462464, 4960547004924886375/534362651099136, ...

%t V[n_] := (4 n - 1)!!/(4!^n n!);

%t Table[V[n] // Numerator, {n, 0, 16}] (* _Jean-François Alcover_, Sep 05 2018 *)

%Y Cf. A225698.

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_, May 30 2013