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A328923 Triangle T(n,k) read by rows: connected topologies of Goldstone diagrams with n interactions and k external potentials.

%I A328923 #4 Oct 31 2019 07:56:36
%S A328923 1,2,1,6,4,1,76,60,18,2,2124,1776,600,96,6,97968,84720,31080,6000,600,
%T A328923 24,6624720,5876640,2287440,497280,63000,4320,120,615022560,556466400,
%U A328923 226250640,53373600,7832160,705600,35280,720,74975211360,68882446080,28936252800,7240020480
%N A328923 Triangle T(n,k) read by rows: connected topologies of Goldstone diagrams with n interactions and k external potentials.
%H A328923 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, T(n,k)
%F A328923 T(n,0) = A328921(n,0) / 2^n +(n-1)! .
%F A328923 T(n,k) = 2^(k-n)*A328921(n,k), k>0 .
%e A328923          1;
%e A328923          2          1;
%e A328923          6          4          1;
%e A328923         76         60         18          2;
%e A328923       2124       1776        600         96          6;
%e A328923      97968      84720      31080       6000        600         24;
%e A328923    6624720    5876640    2287440     497280      63000       4320        120;
%Y A328923 Cf. A328921-A328924
%K A328923 nonn,tabl
%O A328923 0,2
%A A328923 _R. J. Mathar_, Oct 31 2019