cp's OEIS Frontend

A001507 a(n) is the number of c-nets with n+1 vertices and 2n+1 edges, n >= 1.

%I A001507 M3132 N1270 #39 Jul 28 2017 09:38:08
%S A001507 0,0,0,3,33,338,3580,39525,452865,5354832,65022840,807560625,
%T A001507 10224817515,131631305718,1719292293940,22743461653913,
%U A001507 304256251541865,4111134671255120,56049154766899216,770325744569310630,10664613057653024586,148625522045319923940
%N A001507 a(n) is the number of c-nets with n+1 vertices and 2n+1 edges, n >= 1.
%D A001507 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001507 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001507 Gheorghe Coserea, <a href="/A001507/b001507.txt">Table of n, a(n) for n = 1..203</a>
%H A001507 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 A001507 a(n) = A290326(n+1,n). - _Sean A. Irvine_, Sep 29 2015
%o A001507 (PARI)
%o A001507 A290326(n,k) = {
%o A001507   if (n < 3 || k < 3, return(0));
%o A001507   sum(i=0, k-1, sum(j=0, n-1,
%o A001507      (-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*
%o A001507      (binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -
%o A001507       4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));
%o A001507 };
%o A001507 vector(22, n, A290326(n+1,n)) \\ _Gheorghe Coserea_, Jul 28 2017
%Y A001507 Cf. A290326.
%K A001507 nonn
%O A001507 1,4
%A A001507 _N. J. A. Sloane_
%E A001507 Corrected and extended by _Sean A. Irvine_, Sep 29 2015
%E A001507 Name changed by _Gheorghe Coserea_, Jul 23 2017