A214298 Number of n-th order connected Feynman diagrams.

1, 4, 80, 3552, 271104, 31342080, 5087692800, 1102119137280, 307098445086720, 107024623079915520, 45623072462929920000, 23361142846626437529600, 14152553458020435728793600, 10014464602019135560561459200, 8186110540477899728656269312000

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

F. Battaglia, T. F. George, A Pascal type triangle for the number of topologically distinct many-electron Feynman diagrams, J. Math. Chem. 2 (1988) 241-247, Function C(n)

Formula

a(n) = n!*2^n*A000698(n+1).

a(n) = A000142(n)*A000079(n)*A000698(n+1) = A000165(n)*A000698(n+1). - Omar E. Pol, Jul 11 2012

Maple

b:= proc(x, y, t) option remember; `if`(y>x or y<0, 0,
      `if`(x=0, 1, b(x-1, y-1, false)*`if`(t, (x+y)/y, 1) +
                   b(x-1, y+1, true)  ))
    end:
a:= n-> n!*2^n*b(2*n, 0, false):
seq(a(n), n=0..15);  # Alois P. Heinz, May 23 2015

Mathematica

b[x_, y_, t_] := b[x, y, t] = If[y>x || y<0, 0, If[x == 0, 1, b[x-1, y-1, False] * If[t, (x+y)/y, 1] + b[x-1, y+1, True]]]; a[n_] := n!*2^n*b[2*n, 0, False]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jun 22 2015, after Alois P. Heinz *)

Crossrefs

Main diagonal of A214299.

Sequence in context: A268734 A012824 A012057 * A102063 A002436 A013031

Adjacent sequences: A214295 A214296 A214297 * A214299 A214300 A214301

Keyword

nonn,easy

Author

R. J. Mathar, Jul 11 2012

Status

approved