A245767 Triangular array read by rows: T(n,k) is the number of transitive relations on {1,2,...,n} that have exactly k reflexive points, n>=0, 0<=k<=n.

1, 1, 1, 3, 6, 4, 19, 57, 66, 29, 219, 876, 1428, 1116, 355, 4231, 21155, 44500, 49070, 28405, 6942, 130023, 780138, 2013810, 2858700, 2354415, 1068576, 209527, 6129859, 42909013, 131457522, 228345565, 242894155, 158322528, 58628647, 9535241

Offset

0,4

Comments

Row sums give A006905.

Column k=0 is A001035.

T(n,n) = A000798(n).

Links

Alois P. Heinz, Rows n = 0..18, flattened

Formula

E.g.f.: A(x + exp(y*x) - 1) where A(x) is the e.g.f. for A001035.

Example

T(2,1) = 6 because we have: {(1,1)}, {(2,2)}, {(1,1),(1,2)}, {(1,1),(2,1)}, {(2,2),(1,2)}, {(2,2),(2,1)}.
Triangle T(n,k) begins:
       1;
       1,      1;
       3,      6,       4;
      19,     57,      66,      29;
     219,    876,    1428,    1116,     355;
    4231,  21155,   44500,   49070,   28405,    6942;
  130023, 780138, 2013810, 2858700, 2354415, 1068576, 209527;
  ...

Mathematica

A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];
lg = Length[A001035];
A[x_] = Sum[A001035[[n+1]] x^n/n!, {n, 0, lg-1}];
CoefficientList[#, y]& /@ (CoefficientList[A[x + Exp[y*x]-1] + O[x]^lg, x]* Range[0, lg-1]!) // Flatten (* Jean-François Alcover, Jan 01 2020 *)

Crossrefs

Cf. A000798, A001035, A006905.

Sequence in context: A307460 A128719 A145691 * A367302 A009782 A294670

Adjacent sequences: A245764 A245765 A245766 * A245768 A245769 A245770

Keyword

nonn,tabl

Author

Geoffrey Critzer, Jul 31 2014

Status

approved