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

0,5

Comments

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

Links

Table of n, a(n) for n=0..54.

Example

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

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 *)

Prog

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

Crossrefs

Row sums are A136727.

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

Sequence in context: A364068 A293881 A362308 * A268434 A010107 A324429

Adjacent sequences: A185282 A185283 A185284 * A185286 A185287 A185288

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 22 2011

Extensions

More terms from Jean-François Alcover, Jun 25 2019

Status

approved