A256549 - OEIS

%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