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A259876
Triangle of numbers S(n,k) (0 <= k <= n) arising in the enumeration of interval orders without duplicated holdings.
0
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
0,4
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]
FORMULA
T(n,k) = qfactorial(n)/qfactorial(k)*(-1)^(k), n>=k, where qfactorial(n) is A005329. - Vladimir Kruchinin, Feb 17 2020
EXAMPLE
Triangle begins:
1;
1, -1;
3, -3, 1;
21, -21, 7, -1;
315, -315, 105, -15, 1;
9765, -9765, 3255, -465, 31, -1;
...
CROSSREFS
Row sums give A005327.
Column k=0 gives A005329.
Main diagonal gives A033999.
T(n+1,n) gives A225883(n+1).
Sequence in context: A111840 A174031 A228859 * A276402 A318110 A117262
KEYWORD
sign,tabl
AUTHOR
N. J. A. Sloane, Jul 09 2015
EXTENSIONS
More terms from Alois P. Heinz, Feb 17 2020
STATUS
approved