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

0,8

Links

Table of n, a(n) for n=0..65.

Peter Luschny, The Bell transform

Example

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]

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 *)

Prog

(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)

Crossrefs

Cf. A000110, A187761, A264428.

Sequence in context: A256550 A005210 A352363 * A264433 A132393 A048994

Adjacent sequences: A264427 A264428 A264429 * A264431 A264432 A264433

Keyword

nonn,tabl

Author

Peter Luschny, Nov 13 2015

Status

approved