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

0, 0, 0, 3, 33, 338, 3580, 39525, 452865, 5354832, 65022840, 807560625, 10224817515, 131631305718, 1719292293940, 22743461653913, 304256251541865, 4111134671255120, 56049154766899216, 770325744569310630, 10664613057653024586, 148625522045319923940

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Gheorghe Coserea, Table of n, a(n) for n = 1..203
• R. C. Mullin and P. J. Schellenberg, The enumeration of c-nets via triangulations, J. Combin. Theory, 4 (1968), 259-276.

Crossrefs

Cf. A290326.

Programs

PARI

A290326(n,k) = {
  if (n < 3 || k < 3, return(0));
  sum(i=0, k-1, sum(j=0, n-1,
     (-1)^((i+j+1)%2) * binomial(i+j, i)*(i+j+1)*(i+j+2)/2*
     (binomial(2*n, k-i-1) * binomial(2*k, n-j-1) -
      4 * binomial(2*n-1, k-i-2) * binomial(2*k-1, n-j-2))));
};
vector(22, n, A290326(n+1,n)) \\ Gheorghe Coserea, Jul 28 2017

Formula

a(n) = A290326(n+1,n). - Sean A. Irvine, Sep 29 2015

Extensions

Corrected and extended by Sean A. Irvine, Sep 29 2015

Name changed by Gheorghe Coserea, Jul 23 2017