A328924 - OEIS

%I #3 Oct 31 2019 07:59:29

%S 1,0,1,2,0,1,12,12,6,2,300,336,168,48,6,13680,15120,7560,2160,360,24,

%T 920400,1000800,498960,146880,27000,2880,120,85004640,91314720,

%U 45516240,13698720,2691360,342720,25200,720,10314511200,10981474560,5476625280,1675699200,344433600,48545280,4515840,241920,5040

%N Triangle T(n,k) read by rows: connected topologies of the effective potential in Goldstone diagrams with n interactions and k external potentials.

%H P. J. Rossky, M. Karplus, <a href="https://doi.org/10.1063/1.432387">The enumeration of Goldstone diagrams in many-body perturbation theory</a>, J. Chem. Phys. 64 (1976) 1569, Teff(n,k)

%F T(n,k) = sum_{t=k..n} (-1)^(k+t) *2^(t-k) *binomial(t,k) *A328923(n,t).

%e          1;

%e          0          1;

%e          2          0          1;

%e         12         12          6          2;

%e        300        336        168         48          6;

%e      13680      15120       7560       2160        360         24;

%e     920400    1000800     498960     146880      27000       2880        120;

%e   85004640   91314720   45516240   13698720    2691360     342720      25200        720;

%Y Cf. A328921-A328923.

%K nonn,tabl

%O 0,4

%A _R. J. Mathar_, Oct 31 2019