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A256549 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.

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