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