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A264433 Triangle read by rows, Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.

%I A264433 #22 Jan 30 2021 02:12:42
%S A264433 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 A264433 0,700,1757,1624,735,175,21,1,0,4748,12880,13104,6769,1960,322,28,1,0,
%U A264433 36403,106068,117152,67200,22449,4536,546,36,1,0,310851,968206,1150050,720020,269115,63273,9450,870,45,1
%N A264433 Triangle read by rows, Bell transform of the third-order Bell numbers, T(n,k) for n >= 0 and 0 <= k <= n.
%e A264433 [1]
%e A264433 [0,     1]
%e A264433 [0,     1,      1]
%e A264433 [0,     2,      3,      1]
%e A264433 [0,     6,     11,      6,     1]
%e A264433 [0,    24,     50,     35,    10,     1]
%e A264433 [0,   119,    274,    225,    85,    15,    1]
%e A264433 [0,   700,   1757,   1624,   735,   175,   21,   1]
%e A264433 [0,  4748,  12880,  13104,  6769,  1960,  322,  28,  1]
%e A264433 [0, 36403, 106068, 117152, 67200, 22449, 4536, 546, 36, 1]
%o A264433 (Sage) # uses[bell_transform from A264428]
%o A264433 def A264433_triangle(dim):
%o A264433     uno = [1]*dim
%o A264433     bell_number = [sum(bell_transform(n, uno)) for n in range(dim)]
%o A264433     bell_number_2 = [sum(bell_transform(n, bell_number)) for n in range(dim)]
%o A264433     bell_number_3 = [sum(bell_transform(n, bell_number_2)) for n in range(dim)]
%o A264433     for n in range(dim): print(bell_transform(n, bell_number_3))
%o A264433 A264433_triangle(10)
%Y A264433 Cf. A000110, A048993, A264428, A264430.
%K A264433 nonn,tabl
%O A264433 0,8
%A A264433 _Peter Luschny_, Dec 02 2015
%E A264433 More terms from _Michel Marcus_, Mar 27 2020