A079510 Triangle T(n,k) read by rows; related to number of preorders.

1, 0, 2, 0, 3, 6, 0, 0, 20, 24, 0, 0, 15, 130, 120, 0, 0, 0, 210, 924, 720, 0, 0, 0, 105, 2380, 7308, 5040, 0, 0, 0, 0, 2520, 26432, 64224, 40320, 0, 0, 0, 0, 945, 44100, 303660, 623376, 362880, 0, 0, 0, 0, 0, 34650, 705320, 3678840, 6636960, 3628800

Offset: 1

Author

N. J. A. Sloane, Jan 21 2003

Keywords

• nonn
• tabl

Comments

There are only m nonzero entries in the m-th column.

Examples

			Triangle begins:
  1;
  0,   2;
  0,   3,   6;
  0,   0,  20,  24;
  0,   0,  15, 130, 120;
  ...
		

Links

• G. C. Greubel, Rows n=1..30 of triangle, flattened
• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30. (See the array on page 29.)
• G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30. (Annotated scanned copy)

Crossrefs

A rearrangement of the triangle in A008306. - Benoit Cloitre, Jan 27 2003

Programs

Mathematica

T[n_, k_]:= If[k < 1 || k > n, 0, If[n==1 && k==1, 1, n*(T[n-1, k-1] + T[n-2, k-1])]]; Table[T[n, k], {n, 1, 10}, {k, 1, n}]//Flatten (* G. C. Greubel, Jan 17 2019 *)

PARI

T(n,k)=if(k<=0 || k>n, 0, if(n==1 && k==1, 1, n*(T(n-1,k-1)+T(n-2,k-1))));

Extensions

Recurrence and more terms from Michael Somos, Jan 23 2003

Offset changed to 1 by G. C. Greubel, Jan 17 2019