A001506 - OEIS

%I M3603 N1462 #40 Jul 28 2017 09:38:40

%S 0,0,1,4,24,188,1705,16980,180670,2020120,23478426,281481880,

%T 3461873536,43494961404,556461656569,7230987646484,95244774132810,

%U 1269534571172912,17100621281619328,232511930087682528,3188042426888493288

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Gheorghe Coserea, <a href="/A001506/b001506.txt">Table of n, a(n) for n = 1..200</a>

%H 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 a(n) = A290326(n,n). - _Sean A. Irvine_, Sep 29 2015

%o (PARI)

%o A290326(n,k) = {

%o   if (n < 3 || k < 3, return(0));

%o   sum(i=0, k-1, sum(j=0, n-1,

%o      (-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*

%o      (binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -

%o       4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));

%o };

%o vector(21, n, A290326(n,n))  \\ _Gheorghe Coserea_, Jul 28 2017

%Y Cf. A290326.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E Corrected and extended by _Sean A. Irvine_, Sep 29 2015

%E Name changed by _Gheorghe Coserea_, Jul 23 2017