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A328924
Triangle T(n,k) read by rows: connected topologies of the effective potential in Goldstone diagrams with n interactions and k external potentials.
3
1, 0, 1, 2, 0, 1, 12, 12, 6, 2, 300, 336, 168, 48, 6, 13680, 15120, 7560, 2160, 360, 24, 920400, 1000800, 498960, 146880, 27000, 2880, 120, 85004640, 91314720, 45516240, 13698720, 2691360, 342720, 25200, 720, 10314511200, 10981474560, 5476625280, 1675699200, 344433600, 48545280, 4515840, 241920, 5040
OFFSET
0,4
LINKS
P. J. Rossky, M. Karplus, The enumeration of Goldstone diagrams in many-body perturbation theory, J. Chem. Phys. 64 (1976) 1569, Teff(n,k)
FORMULA
T(n,k) = sum_{t=k..n} (-1)^(k+t) *2^(t-k) *binomial(t,k) *A328923(n,t).
EXAMPLE
1;
0 1;
2 0 1;
12 12 6 2;
300 336 168 48 6;
13680 15120 7560 2160 360 24;
920400 1000800 498960 146880 27000 2880 120;
85004640 91314720 45516240 13698720 2691360 342720 25200 720;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Oct 31 2019
STATUS
approved