OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
Eric Weisstein's World of Mathematics, Minimal Dominating Set
Eric Weisstein's World of Mathematics, Rook Graph
FORMULA
T(m, n) = T(n, m).
T(n, k) = k^n + n^k - k! * stirling2(n,k) for k<=n.
EXAMPLE
Array begins:
========================================================
m\n| 1 2 3 4 5 6 7 8
---|----------------------------------------------------
1 | 1 2 3 4 5 6 7 8 ...
2 | 2 6 11 18 27 38 51 66 ...
3 | 3 11 48 109 218 405 724 1277 ...
4 | 4 18 109 488 1409 3832 10385 28808 ...
5 | 5 27 218 1409 6130 21601 78132 297393 ...
6 | 6 38 405 3832 21601 92592 382465 1750240 ...
7 | 7 51 724 10385 78132 382465 1642046 7720833 ...
8 | 8 66 1277 28808 297393 1750240 7720833 33514112 ...
...
MATHEMATICA
T[m_, n_] := m^n + n^m - Min[m, n]! StirlingS2[Max[m, n], Min[m, n]] (* Eric W. Weisstein, Aug 10 2017 *)
PROG
(PARI)
T(m, n) = m^n + n^m - if(n<=m, n!*stirling(m, n, 2), m!*stirling(n, m, 2));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Aug 07 2017
STATUS
approved