|
|
A001507
|
|
a(n) is the number of c-nets with n+1 vertices and 2n+1 edges, n >= 1.
(Formerly M3132 N1270)
|
|
3
|
|
|
0, 0, 0, 3, 33, 338, 3580, 39525, 452865, 5354832, 65022840, 807560625, 10224817515, 131631305718, 1719292293940, 22743461653913, 304256251541865, 4111134671255120, 56049154766899216, 770325744569310630, 10664613057653024586, 148625522045319923940
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
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
|
|
|
FORMULA
|
|
|
PROG
|
(PARI)
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))));
};
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|