OFFSET
0,2
COMMENTS
Equivalently, a(n) is the number of n x n binary relation matrices such that each of the blocks above the diagonal of its Frobenius normal form is a 1-block (a block containing all 1's). See Gregory, Kirkland and Pullman for definition of Frobenius normal form.
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.
FORMULA
E.g.f.: 1/(1-(s(2x)-1)) where s(x) is the e.g.f. for A003030.
MATHEMATICA
nn = 11; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
Length@# == 2 &][[All, 2]]; s[x_] := Total[Prepend[strong Table[x^i/i!, {i, 1, 58}], 1]]; Table[n!, {n, 0, nn}] CoefficientList[Series[1/(1 - (s[x + x] - 1)), {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 07 2023
STATUS
approved