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

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, 0, 568, 1645, 1603, 735, 175, 21, 1, 0, 3459, 11348, 12572, 6713, 1960, 322, 28, 1, 0, 23544, 86775, 107738, 65352, 22323, 4536, 546, 36, 1, 0, 176850, 727629, 1001895, 678980, 263865, 63021, 9450, 870, 45, 1

Offset: 0

Author

Peter Luschny, Nov 13 2015

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[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]
[0,  568,  1645,  1603,  735,  175,  21,  1]
[0, 3459, 11348, 12572, 6713, 1960, 322, 28, 1]
		

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000110, A187761, A264428.

Programs

Mathematica

nmax = 10;
A187761[n_] := Sum[BellY[n, k, BellB /@ Range[0, n-1]], {k, 0, n}];
Table[BellY[n, k, A187761 /@ Range[0, nmax]], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 10 2019 *)

Sage

# uses[bell_transform from A264428]
def A264430_triangle(dim):
    uno = [1]*dim
    bell_numbers = [sum(bell_transform(n, uno)) for n in range(dim)]
    bell_number_2 = [sum(bell_transform(n, bell_numbers)) for n in range(dim)]
    for n in range(dim): print(bell_transform(n, bell_number_2))
A264430_triangle(10)