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

%I A259876 #23 Feb 17 2020 08:07:09
%S A259876 1,1,-1,3,-3,1,21,-21,7,-1,315,-315,105,-15,1,9765,-9765,3255,-465,31,
%T A259876 -1,615195,-615195,205065,-29295,1953,-63,1,78129765,-78129765,
%U A259876 26043255,-3720465,248031,-8001,127,-1,19923090075,-19923090075,6641030025,-948718575,63247905,-2040255,32385,-255,1
%N A259876 Triangle of numbers S(n,k) (0 <= k <= n) arising in the enumeration of interval orders without duplicated holdings.
%D A259876 T. L. Greenough, Enumeration of interval orders without duplicated holdings, Preprint, circa 1976.
%H A259876 T. L. Greenough, <a href="/A005321/a005321_1.pdf">Enumeration of interval orders without duplicated holdings</a>, Preprint, circa 1976. [Annotated scanned copy]
%H A259876 T. L. Greenough, <a href="https://www.ams.org/journals/notices/197602/197602FullIssue.pdf">Enumeration of interval orders without duplicated holdings</a>, Notices of the AMS, Vol 23-2, February 1976, Issue 168, pages A-314 and A-315. [Mentions this paper]
%F A259876 T(n,k) = qfactorial(n)/qfactorial(k)*(-1)^(k), n>=k, where qfactorial(n) is A005329. - _Vladimir Kruchinin_, Feb 17 2020
%e A259876 Triangle begins:
%e A259876      1;
%e A259876      1,    -1;
%e A259876      3,    -3,    1;
%e A259876     21,   -21,    7,   -1;
%e A259876    315,  -315,  105,  -15,  1;
%e A259876   9765, -9765, 3255, -465, 31, -1;
%e A259876   ...
%Y A259876 Row sums give A005327.
%Y A259876 Column k=0 gives A005329.
%Y A259876 Main diagonal gives A033999.
%Y A259876 T(n+1,n) gives A225883(n+1).
%K A259876 sign,tabl
%O A259876 0,4
%A A259876 _N. J. A. Sloane_, Jul 09 2015
%E A259876 More terms from _Alois P. Heinz_, Feb 17 2020