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

1, 2, 1, 6, 4, 1, 76, 60, 18, 2, 2124, 1776, 600, 96, 6, 97968, 84720, 31080, 6000, 600, 24, 6624720, 5876640, 2287440, 497280, 63000, 4320, 120, 615022560, 556466400, 226250640, 53373600, 7832160, 705600, 35280, 720, 74975211360, 68882446080, 28936252800, 7240020480

Offset

0,2

Links

Table of n, a(n) for n=0..39.

P. J. Rossky, M. Karplus, The enumeration of Goldstone diagrams in many-body perturbation theory, J. Chem. Phys. 64 (1976) 1569, T(n,k)

Formula

T(n,0) = A328921(n,0) / 2^n +(n-1)! .

T(n,k) = 2^(k-n)*A328921(n,k), k>0 .

Example

         1;
         2          1;
         6          4          1;
        76         60         18          2;
      2124       1776        600         96          6;
     97968      84720      31080       6000        600         24;
   6624720    5876640    2287440     497280      63000       4320        120;

Crossrefs

Cf. A328921-A328924

Sequence in context: A162312 A141715 A329431 * A263271 A098697 A193094

Adjacent sequences: A328920 A328921 A328922 * A328924 A328925 A328926

Keyword

nonn,tabl

Author

R. J. Mathar, Oct 31 2019

Status

approved