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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
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
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
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Jul 24 2015
STATUS
approved