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%I #22 Jan 30 2021 02:12:42
%S 1,0,1,0,1,1,0,2,3,1,0,6,11,6,1,0,24,50,35,10,1,0,119,274,225,85,15,1,
%T 0,700,1757,1624,735,175,21,1,0,4748,12880,13104,6769,1960,322,28,1,0,
%U 36403,106068,117152,67200,22449,4536,546,36,1,0,310851,968206,1150050,720020,269115,63273,9450,870,45,1
%N Triangle read by rows, Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.
%e [1]
%e [0, 1]
%e [0, 1, 1]
%e [0, 2, 3, 1]
%e [0, 6, 11, 6, 1]
%e [0, 24, 50, 35, 10, 1]
%e [0, 119, 274, 225, 85, 15, 1]
%e [0, 700, 1757, 1624, 735, 175, 21, 1]
%e [0, 4748, 12880, 13104, 6769, 1960, 322, 28, 1]
%e [0, 36403, 106068, 117152, 67200, 22449, 4536, 546, 36, 1]
%o (Sage) # uses[bell_transform from A264428]
%o def A264433_triangle(dim):
%o uno = [1]*dim
%o bell_number = [sum(bell_transform(n, uno)) for n in range(dim)]
%o bell_number_2 = [sum(bell_transform(n, bell_number)) for n in range(dim)]
%o bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
%o for n in range(dim): print(bell_transform(n, bell_number_3))
%o A264433_triangle(10)
%Y Cf. A000110, A048993, A264428, A264430.
%K nonn,tabl
%O 0,8
%A _Peter Luschny_, Dec 02 2015
%E More terms from _Michel Marcus_, Mar 27 2020
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