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A264430 Triangle read by rows, Bell transform of second order Bell numbers (A187761).

%I A264430 #19 Mar 28 2020 05:27:29
%S A264430 1,0,1,0,1,1,0,2,3,1,0,6,11,6,1,0,23,50,35,10,1,0,106,268,225,85,15,1,
%T A264430 0,568,1645,1603,735,175,21,1,0,3459,11348,12572,6713,1960,322,28,1,0,
%U A264430 23544,86775,107738,65352,22323,4536,546,36,1,0,176850,727629,1001895,678980,263865,63021,9450,870,45,1
%N A264430 Triangle read by rows, Bell transform of second order Bell numbers (A187761).
%H A264430 Peter Luschny, <a href="https://oeis.org/wiki/User:Peter_Luschny/BellTransform">The Bell transform</a>
%e A264430 Triangle starts:
%e A264430 [1]
%e A264430 [0,    1]
%e A264430 [0,    1,     1]
%e A264430 [0,    2,     3,     1]
%e A264430 [0,    6,    11,     6,    1]
%e A264430 [0,   23,    50,    35,   10,    1]
%e A264430 [0,  106,   268,   225,   85,   15,   1]
%e A264430 [0,  568,  1645,  1603,  735,  175,  21,  1]
%e A264430 [0, 3459, 11348, 12572, 6713, 1960, 322, 28, 1]
%t A264430 nmax = 10;
%t A264430 A187761[n_] := Sum[BellY[n, k, BellB /@ Range[0, n-1]], {k, 0, n}];
%t A264430 Table[BellY[n, k, A187761 /@ Range[0, nmax]], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 10 2019 *)
%o A264430 (Sage) # uses[bell_transform from A264428]
%o A264430 def A264430_triangle(dim):
%o A264430     uno = [1]*dim
%o A264430     bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
%o A264430     bell_number_2 = [sum(bell_transform(n, bell_numbers)) for n in range(dim)]
%o A264430     for n in range(dim): print(bell_transform(n, bell_number_2))
%o A264430 A264430_triangle(10)
%Y A264430 Cf. A000110, A187761, A264428.
%K A264430 nonn,tabl
%O A264430 0,8
%A A264430 _Peter Luschny_, Nov 13 2015