A260383 Triangle read by rows: number of spanning trees obtained for an almost-complete bipartite graph by removing k disjoint edges from the complete bipartite graph K n,n with k<=n.

0, 1, 0, 36, 15, 6, 2304, 1280, 704, 384, 250000, 159375, 101250, 64125, 40500, 41990400, 29113344, 20155392, 13934592, 9621504, 6635520, 10169108964, 7465417295, 5476560950, 4014772125, 2941225000, 2153396875, 1575656250, 3367254360064, 2576980377600

Offset

1,4

Links

Table of n, a(n) for n=1..30.

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

Sequence in context: A066583 A073405 A298572 * A056770 A061038 A058231

Adjacent sequences: A260380 A260381 A260382 * A260384 A260385 A260386

Keyword

nonn,tabl

Author

Michel Marcus, Jul 24 2015

Status

approved