A259876 Triangle of numbers S(n,k) (0 <= k <= n) arising in the enumeration of interval orders without duplicated holdings.

1, 1, -1, 3, -3, 1, 21, -21, 7, -1, 315, -315, 105, -15, 1, 9765, -9765, 3255, -465, 31, -1, 615195, -615195, 205065, -29295, 1953, -63, 1, 78129765, -78129765, 26043255, -3720465, 248031, -8001, 127, -1, 19923090075, -19923090075, 6641030025, -948718575, 63247905, -2040255, 32385, -255, 1

Offset: 0

Author

N. J. A. Sloane, Jul 09 2015

Keywords

• sign
• tabl

Examples

			Triangle begins:
     1;
     1,    -1;
     3,    -3,    1;
    21,   -21,    7,   -1;
   315,  -315,  105,  -15,  1;
  9765, -9765, 3255, -465, 31, -1;
  ...
		

References

• T. L. Greenough, Enumeration of interval orders without duplicated holdings, Preprint, circa 1976.

Links

• T. L. Greenough, Enumeration of interval orders without duplicated holdings, Preprint, circa 1976. [Annotated scanned copy]
• T. L. Greenough, Enumeration of interval orders without duplicated holdings, Notices of the AMS, Vol 23-2, February 1976, Issue 168, pages A-314 and A-315. [Mentions this paper]

Crossrefs

Row sums give A005327.

Column k=0 gives A005329.

Main diagonal gives A033999.

T(n+1,n) gives A225883(n+1).

Formula

T(n,k) = qfactorial(n)/qfactorial(k)*(-1)^(k), n>=k, where qfactorial(n) is A005329. - Vladimir Kruchinin, Feb 17 2020

Extensions

More terms from Alois P. Heinz, Feb 17 2020