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%I #6 Jan 22 2024 05:54:09
%S 1,0,2,0,3,12,0,4,60,120,0,5,210,1260,1680,0,6,630,8400,30240,30240,0,
%T 7,1736,45360,327600,831600,665280,0,8,4536,216720,2772000,13305600,
%U 25945920,17297280,0,9,11430,956340,20207880,162162000,575134560,908107200,518918400
%N Table read by rows: T(n, k) = A124320(n + 1, k) * A048993(n, k).
%e Triangle starts:
%e [0] [1]
%e [1] [0, 2]
%e [2] [0, 3, 12]
%e [3] [0, 4, 60, 120]
%e [4] [0, 5, 210, 1260, 1680]
%e [5] [0, 6, 630, 8400, 30240, 30240]
%e [6] [0, 7, 1736, 45360, 327600, 831600, 665280]
%e [7] [0, 8, 4536, 216720, 2772000, 13305600, 25945920, 17297280]
%o (SageMath)
%o def Trow(n): return [rising_factorial(n+1, k)*stirling_number2(n, k)
%o for k in range(n+1)]
%o for n in range(7): print(Trow(n))
%Y Cf. A124320 (rising factorial), A048993(Stirling2), A053492 (row sums), A213236 (alternating row sums), A001813 (main diagonal), A368583.
%K nonn,tabl
%O 0,3
%A _Peter Luschny_, Jan 10 2024