OFFSET
0,3
COMMENTS
Equivalently, a(n) is the number of binary relations R on [n] such that the Frobenius normal form has no 0-blocks on the diagonal and all off diagonal blocks are 0-blocks.
LINKS
D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
S. Schwarz, On the semigroup of binary relations on a finite set , Czechoslovak Mathematical Journal, 1970.
FORMULA
E.g.f.: exp(s(2x)-x) where s(x) is the e.g.f. for A003030.
MATHEMATICA
nn = 12; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]];
Table[n!, {n, 0, nn}] CoefficientList[Series[Exp [s[2 x] - x], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 22 2024
STATUS
approved