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%I #7 Apr 12 2015 17:36:17
%S 1,0,1,0,1,3,0,1,9,13,0,1,21,78,73,0,1,45,325,730,501,0,1,93,1170,
%T 4745,7515,4051,0,1,189,3913,25550,70140,85071,37633,0,1,381,12558,
%U 124173,526050,1077566,1053724,394353,0,1,765,39325,567210,3482451,10718946,17386446,14196708,4596553
%N Triangle read by rows, T(n,k) = {n,k}*h(k), where {n,k} are the Stirling set numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.
%F Row sums are A075729.
%F Alternating row sums are the signed Bell numbers (-1)^n*A000110(n).
%F T(n,k) = A048993(n,k)*A000262(k).
%F T(n,n) = A000262(n).
%F T(n+2,2) = A068156(n).
%e Triangle starts:
%e [1]
%e [0, 1]
%e [0, 1, 3]
%e [0, 1, 9, 13]
%e [0, 1, 21, 78, 73]
%e [0, 1, 45, 325, 730, 501]
%e [0, 1, 93, 1170, 4745, 7515, 4051]
%o (Sage)
%o A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
%o A256549 = lambda n,k: A000262(k)*stirling_number2(n,k)
%o for n in range(7): [A256549(n,k) for k in (0..n)]
%Y Cf. A000110, A000262, A048993, A068156, A075729.
%K nonn,tabl,easy
%O 0,6
%A _Peter Luschny_, Apr 12 2015
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