cp's OEIS Frontend

A001508 a(n) is the number of c-nets with n+1 vertices and 2n+2 edges, n >= 1.

%I A001508 M4918 N2111 #37 Jul 28 2017 09:38:50
%S A001508 0,0,0,0,13,252,3740,51300,685419,9095856,120872850,1614234960,
%T A001508 21697730835,293695935764,4003423965684,54944523689692,
%U A001508 758990230992175,10548884795729280,147458773053913268,2072369440050644208,29271357456284966994
%N A001508 a(n) is the number of c-nets with n+1 vertices and 2n+2 edges, n >= 1.
%D A001508 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001508 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001508 Gheorghe Coserea, <a href="/A001508/b001508.txt">Table of n, a(n) for n = 1..204</a>
%H A001508 R. C. Mullin and P. J. Schellenberg, <a href="http://dx.doi.org/10.1016/S0021-9800(68)80007-9">The enumeration of c-nets via triangulations</a>, J. Combin. Theory, 4 (1968), 259-276.
%F A001508 a(n) = A290326(n+2,n). - _Gheorghe Coserea_, Jul 28 2017
%o A001508 (PARI)
%o A001508 A290326(n,k) = {
%o A001508   if (n < 3 || k < 3, return(0));
%o A001508   sum(i=0, k-1, sum(j=0, n-1,
%o A001508      (-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*
%o A001508      (binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -
%o A001508       4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));
%o A001508 };
%o A001508 vector(21, n, A290326(n+2,n)) \\ _Gheorghe Coserea_, Jul 28 2017
%Y A001508 Cf. A290326.
%K A001508 nonn
%O A001508 1,5
%A A001508 _N. J. A. Sloane_
%E A001508 Corrected and extended by _Sean A. Irvine_, Sep 29 2015
%E A001508 Name changed by _Gheorghe Coserea_, Jul 23 2017