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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.
2
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
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
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jul 31 2014
STATUS
approved