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A226259 Denominators of mass formula for connected vacuum graphs on n nodes for a phi^4 field theory. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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.

FORMULA

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

EXAMPLE

1, 1/8, 1/12, 11/96, 17/72, 619/960, 709/324, ...

PROG

(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 */

CROSSREFS

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

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jun 02 2013

EXTENSIONS

More terms from Franck Maminirina Ramaharo, Feb 04 2019

STATUS

approved

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Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)