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%I #14 Feb 04 2019 09:10:27
%S 1,5,5,1105,565,82825,19675,1282031525,80727925,1683480621875,
%T 13209845125,2239646759308375,19739117098375,6320791709083309375,
%U 32468078556378125,38362676768845045751875,281365778405032973125,2824650747089425586152484375,776632157034116712734375
%N Numerators of mass formula for connected vacuum graphs on 2n nodes for a phi^3 field theory.
%H Carl. M. Bender and K. A. Milton, <a href="https://arxiv.org/abs/hep-th/9304052">Continued fraction as a discrete nonlinear transform</a>, arXiv:hep-th/9304052, 1993. See Eq. 15.
%H Carl. M. Bender and K. A. Milton, <a href="https://doi.org/10.1063/1.530777">Continued fraction as a discrete nonlinear transform</a>, Journal of Mathematical Physics 35, 1994, 364-367.
%F Let V(n) = (3*n - 1)!!/(3!^n*n!), and c(n) = V(2*n) - (1/n)*Sum_{j=0..n-1} j*c(j)*V(2*(n-j)), c(0) = 1. Then a(n) = numerator of c(n). - _Franck Maminirina Ramaharo_, Feb 04 2019
%e 1, 5/24, 5/16, 1105/1152, 565/128, 82825/3072, 19675/96, 1282031525/688128, 80727925/4096, ...
%o (Maxima)
%o c_list : [1]$
%o V(n) := if n = 0 then 1 else (3*n - 1)!!/(3!^n*n!)$
%o c(n) := V(2*n) - 1/n*sum(j*c_list[j + 1]*V(2*(n - j)), j , 0 , n - 1)$
%o for i:1 thru 50 do c_list : append(c_list, [c(i)])$
%o map(num, c_list); /* _Franck Maminirina Ramaharo_, Feb 04 2019 */
%Y Cf. A226261, A226256, A226256-A226259, A225697, A225698.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Jun 02 2013
%E More terms from _Franck Maminirina Ramaharo_, Feb 04 2019
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