A185285 Triangle T(n,k), read by rows, given by (0, 2, 3, 4, 6, 6, 9, 8, 12, 10, 15, ...) DELTA (1, 0, 1, 0, 1, 0, 1, 0, 1, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 2, 1, 0, 10, 6, 1, 0, 74, 52, 12, 1, 0, 730, 570, 160, 20, 1, 0, 9002, 7600, 2430, 380, 30, 1, 0, 133210, 119574, 42070, 7630, 770, 42, 1, 0, 2299754, 2170252, 822696, 166320, 19740, 1400, 56, 1, 0, 45375130, 44657106, 17985268, 3956568, 528780, 44604, 2352, 72, 1

Offset: 0

Author

Philippe Deléham, Dec 22 2011

Keywords

• nonn
• tabl

Comments

The Bell transform of A004123(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016

Examples

			Triangle begins :
1
0, 1
0, 2, 1
0, 10, 6, 1
0, 74, 52, 12, 1
0, 730, 570, 160, 20, 1
0, 9002, 7600, 2430, 380, 30, 1
0, 133210, 119574, 42070, 7630, 770, 42, 1
		

Crossrefs

Row sums are A136727.

Cf. A000007, A004123, A000012, A002378, A195205.

Programs

Mathematica

(* The function BellMatrix is defined in A264428. *)
a4123[n_] := If[n == 1, 1, PolyLog[-n+1, 2/3]/3];
rows = 10;
M = BellMatrix[a4123[#+1]&, rows];
Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 25 2019 *)

Sage

# uses[bell_matrix from A264428]
bell_matrix(lambda n: A004123(n+1), 10) # Peter Luschny, Jan 18 2016

Extensions

More terms from Jean-François Alcover, Jun 25 2019