OFFSET
0,3
COMMENTS
T(n,n) = 2^n since each node is reflexive or not.
LINKS
Geoffrey Critzer, Finite Topologies
FORMULA
E.g.f.: A(x + exp(x) -1)^y where A(x) is the e.g.f. for A001035.
EXAMPLE
Triangular array T(n,k) begins:
1;
0, 2;
0, 9, 4;
0, 109, 54, 8;
0, 2647, 1115, 216, 16;
0, 110481, 36280, 6790, 720, 32;
...
MATHEMATICA
A[x_] := Total[Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]]* Table[x^(i - 1)/(i - 1)!, {i, 1, 19}]]; nn = 10;
Range[0, nn]! CoefficientList[ Series[Exp[y Log[A[ x + Exp[ x] - 1]]], {x, 0, nn}], {x, y}] // Grid; Table[Take[(Range[0, nn]! CoefficientList[Series[Exp[y Log[A[ x + Exp[ x] - 1]]], {x, 0, nn}], {x, y}])[[i, All]], i], {i, 1, nn}] // Grid
(* Import function in code after Jean-François Alcover *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, May 02 2021
STATUS
approved