A328923 -id:A328923 - cp's OEIS frontend

A328921 Triangle read by rows: T(n,k) = number of vertex labeled connected Goldstone diagrams with n interactions and k external potentials.

1, 2, 1, 20, 8, 1, 592, 240, 36, 2, 33888, 14208, 2400, 192, 6, 3134208, 1355520, 248640, 24000, 1200, 24, 423974400, 188052480, 36599040, 3978240, 252000, 8640, 120, 78722795520, 35613849600, 7240020480, 853977600, 62657280, 2822400, 70560, 720, 19193652817920, 8816953098240, 1851920179200

Offset: 0

R. J. Mathar, Oct 31 2019

			          1;
          2           1;
         20           8           1;
        592         240          36           2;
      33888       14208        2400         192           6;
    3134208     1355520      248640       24000        1200          24;

R. J. Mathar, Maple program computing A328921 - A328924.
P. J. Rossky and M. Karplus, The enumeration of Goldstone diagrams in many-body perturbation theory, J. Chem. Phys. 64 (1976) 1569, C(n,k)

Cf. A328922, A328923, A328924.

T(n,k) + A328922(n,k) = A328826(n,k).

A328924 Triangle T(n,k) read by rows: connected topologies of the effective potential in Goldstone diagrams with n interactions and k external potentials.

Original entry on oeis.org

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

R. J. Mathar, Oct 31 2019

			         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;

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

Cf. A328921-A328923.

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

A328922 Triangle T(n,k): vertex labeled disconnected Goldstone diagrams with n interactions and k external potentials.

Original entry on oeis.org

0, 0, 0, 4, 4, 1, 128, 120, 36, 4, 6432, 5952, 1920, 288, 18, 494592, 458880, 154560, 26400, 2400, 96, 55027200, 51448320, 17832960, 3279360, 352800, 21600, 600, 8455495680, 7975296000, 2819013120, 543110400, 64350720, 4798080, 211680, 4320, 1729137070080, 1644441845760, 589071974400

Offset: 0

R. J. Mathar, Oct 31 2019

			         0;
         0          0;
         4          4          1;
       128        120         36          4;
      6432       5952       1920        288         18;
    494592     458880     154560      26400       2400         96;
  55027200   51448320   17832960    3279360     352800      21600        600;
8455495680 ...

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

Cf. A328826, A328921, A328923, A328924.

T(n,k) + A328921(n,k) = A328826(n,k).

cp's OEIS Frontend

A328921 Triangle read by rows: T(n,k) = number of vertex labeled connected Goldstone diagrams with n interactions and k external potentials.

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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.

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A328922 Triangle T(n,k): vertex labeled disconnected Goldstone diagrams with n interactions and k external potentials.

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