OFFSET
1,4
LINKS
Fuji Zhang and Weigen Yan, Enumerating spanning trees of graphs with an involution, Journal of Combinatorial Theory, Series A, Volume 116, Issue 3, April 2009, Pages 650-662 (see Theorem 4.1).
FORMULA
T(n, k) = ((n-2)*n+k)*(n-2)^(k-1)*n^(2*n-k-3).
EXAMPLE
Triangle begins:
0;
1, 0;
36, 15, 6;
2304, 1280, 704, 384;
250000, 159375, 101250, 64125, 40500;
...
MATHEMATICA
Join[{0, 1, 0}, t[n_, k_]:=((n - 2) n + k) (n - 2)^(k - 1) n^(2 n - k - 3); Table[t[n, k], {n, 3, 10}, {k, n}]//Flatten] (* Vincenzo Librandi, Jul 24 2015 *)
PROG
(PARI) tabl(nn) = {for (n=1, nn, for (p=1, n, print1(((n-2)*n+p)*(n-2)^(p-1)*n^(2*n-p-3), ", "); ); print(); ); }
(Magma) /* As triangle */ [[((n-2)*n+k)*(n-2)^(k-1)*n^(2*n-k-3): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Jul 24 2015
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Jul 24 2015
STATUS
approved