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A214298 Number of n-th order connected Feynman diagrams.

%I A214298 #20 Jun 22 2015 11:37:40
%S A214298 1,4,80,3552,271104,31342080,5087692800,1102119137280,307098445086720,
%T A214298 107024623079915520,45623072462929920000,23361142846626437529600,
%U A214298 14152553458020435728793600,10014464602019135560561459200,8186110540477899728656269312000
%N A214298 Number of n-th order connected Feynman diagrams.
%H A214298 Alois P. Heinz, <a href="/A214298/b214298.txt">Table of n, a(n) for n = 0..200</a>
%H A214298 F. Battaglia, T. F. George, <a href="http://dx.doi.org/10.1007/BF01167204">A Pascal type triangle for the number of topologically distinct many-electron Feynman diagrams</a>, J. Math. Chem. 2 (1988) 241-247, Function C(n)
%F A214298 a(n) = n!*2^n*A000698(n+1).
%F A214298 a(n) = A000142(n)*A000079(n)*A000698(n+1) = A000165(n)*A000698(n+1). - _Omar E. Pol_, Jul 11 2012
%p A214298 b:= proc(x, y, t) option remember; `if`(y>x or y<0, 0,
%p A214298       `if`(x=0, 1, b(x-1, y-1, false)*`if`(t, (x+y)/y, 1) +
%p A214298                    b(x-1, y+1, true)  ))
%p A214298     end:
%p A214298 a:= n-> n!*2^n*b(2*n, 0, false):
%p A214298 seq(a(n), n=0..15);  # _Alois P. Heinz_, May 23 2015
%t A214298 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_ *)
%Y A214298 Main diagonal of A214299.
%K A214298 nonn,easy
%O A214298 0,2
%A A214298 _R. J. Mathar_, Jul 11 2012