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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. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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;

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)}.

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-Fran├žois Alcover, Jan 01 2020 *)

CROSSREFS

Cf. A000798, A001035, A006905.

Sequence in context: A307460 A128719 A145691 * A009782 A294670 A016615

Adjacent sequences:  A245764 A245765 A245766 * A245768 A245769 A245770

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, Jul 31 2014

STATUS

approved

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Last modified January 20 05:23 EST 2020. Contains 331067 sequences. (Running on oeis4.)