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

1,3

Comments

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

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)

Example

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

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 *)

Prog

(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))));

Crossrefs

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

Sequence in context: A334495 A155800 A276658 * A216255 A362788 A262256

Adjacent sequences: A079507 A079508 A079509 * A079511 A079512 A079513

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jan 21 2003

Extensions

Recurrence and more terms from Michael Somos, Jan 23 2003

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

Status

approved