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A256548 Triangle read by rows, T(n,k) = |n,k|*h(k), where |n,k| are the Stirling cycle numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.

%I A256548 #11 Apr 12 2015 13:07:51
%S A256548 1,0,1,0,1,3,0,2,9,13,0,6,33,78,73,0,24,150,455,730,501,0,120,822,
%T A256548 2925,6205,7515,4051,0,720,5292,21112,53655,87675,85071,37633,0,5040,
%U A256548 39204,170716,494137,981960,1304422,1053724,394353
%N A256548 Triangle read by rows, T(n,k) = |n,k|*h(k), where |n,k| are the Stirling cycle numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.
%F A256548 T(n,k) = A132393(n,k)*A000262(k).
%F A256548 T(n,n) = A000262(n).
%F A256548 T(n+1,1) = n!.
%F A256548 Row sums are A088815.
%F A256548 Alternating row sums are (-1)^n*A088819(n).
%e A256548 Triangle starts:
%e A256548 [1]
%e A256548 [0,   1]
%e A256548 [0,   1,   3]
%e A256548 [0,   2,   9,   13]
%e A256548 [0,   6,  33,   78,   73]
%e A256548 [0,  24, 150,  455,  730,  501]
%e A256548 [0, 120, 822, 2925, 6205, 7515, 4051]
%o A256548 (Sage)
%o A256548 A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
%o A256548 A256548 = lambda n,k: A000262(k)*stirling_number1(n,k)
%o A256548 for n in range(7): [A256548(n,k) for k in (0..n)]
%Y A256548 Cf. A000262, A088815, A088819, A132393, A256549.
%K A256548 nonn,tabl,easy
%O A256548 0,6
%A A256548 _Peter Luschny_, Apr 12 2015