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A226259
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Denominators of mass formula for connected vacuum graphs on n nodes for a phi^4 field theory.
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3
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1, 8, 12, 96, 72, 960, 324, 96768, 1296, 82944, 1620, 3649536, 17496, 77635584, 6804, 159252480, 23328, 9746251776, 708588, 392143306752, 2361960, 866843099136, 7794468, 22785590034432, 25509168, 445805022412800, 82904796, 213986410758144, 29760696
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..28.
Carl M. Bender and Kimball A. Milton, Continued fraction as a discrete nonlinear transform, arXiv:hep-th/9304052, 1993. See Eq. 11.
Carl M. Bender and Kimball A. Milton, Continued fraction as a discrete nonlinear transform, Journal of Mathematical Physics 35, 1994, 364-367.
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FORMULA
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Let V(n) = (4*n - 1)!!/(4!^n*n!) = A225697(n)/A225698(n), and c(n) = V(n) - (1/n)*Sum_{j=0..n-1} j*c(j)*V(n-j), c(0) = 1. Then a(n) = denominator of c(n). - Franck Maminirina Ramaharo, Feb 04 2019
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EXAMPLE
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1, 1/8, 1/12, 11/96, 17/72, 619/960, 709/324, ...
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PROG
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(Maxima)
c_list : [1]$
V(n) := if n = 0 then 1 else (4*n - 1)!!/(4!^n*n!)$
c(n) := V(n) - 1/n*sum(j*c_list[j + 1]*V(n - j), j , 0 , n - 1)$
for i:1 thru 50 do c_list : append(c_list, [c(i)])$
map(denom, c_list); /* Franck Maminirina Ramaharo, Feb 04 2019 */
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CROSSREFS
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Cf. A226258, A226256, A226257, A226260, A226261, A225697, A225698.
Sequence in context: A216711 A137232 A147764 * A162466 A098664 A266800
Adjacent sequences: A226256 A226257 A226258 * A226260 A226261 A226262
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane, Jun 02 2013
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EXTENSIONS
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More terms from Franck Maminirina Ramaharo, Feb 04 2019
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STATUS
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approved
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