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A226258 Numerators of mass formula for connected vacuum graphs on n nodes for a phi^4 field theory. 1
1, 1, 1, 11, 17, 619, 709, 858437, 54193, 18639247, 2197187, 33152545703, 1169890097, 41657327595361, 31722037141, 6944870083473751, 10192167279257, 45494616421387671961, 37539803774446801, 249615310568664912892639, 19065529984707154577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..20.

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) = numerator 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(num, c_list); /* Franck Maminirina Ramaharo, Feb 04 2019 */

CROSSREFS

Cf. A226259, A226256, A226257, A226260, A226261, A225697, A225698.

Sequence in context: A146446 A228055 A132092 * A056705 A259744 A065706

Adjacent sequences:  A226255 A226256 A226257 * A226259 A226260 A226261

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 September 29 12:57 EDT 2022. Contains 357090 sequences. (Running on oeis4.)