A226261 - OEIS

%I #13 Feb 04 2019 09:10:41

%S 1,24,16,1152,128,3072,96,688128,4096,7077888,4096,46137344,24576,

%T 436207616,114688,6442450944,2097152,876173328384,9437184,

%U 15668040695808,8388608,138538465099776,1441792,4855443348258816,201326592,1688849860263936,872415232

%N Denominators 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) = denominator 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(denom, c_list); /* _Franck Maminirina Ramaharo_, Feb 04 2019 */

%Y Cf. A226260, 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