%I #21 Mar 28 2020 14:02:49

%S 1,0,1,0,2,1,0,10,6,1,0,74,52,12,1,0,730,570,160,20,1,0,9002,7600,

%T 2430,380,30,1,0,133210,119574,42070,7630,770,42,1,0,2299754,2170252,

%U 822696,166320,19740,1400,56,1,0,45375130,44657106,17985268,3956568,528780,44604,2352,72,1

%N 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.

%C The Bell transform of A004123(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 18 2016

%e Triangle begins :

%e 1

%e 0, 1

%e 0, 2, 1

%e 0, 10, 6, 1

%e 0, 74, 52, 12, 1

%e 0, 730, 570, 160, 20, 1

%e 0, 9002, 7600, 2430, 380, 30, 1

%e 0, 133210, 119574, 42070, 7630, 770, 42, 1

%t (* The function BellMatrix is defined in A264428. *)

%t a4123[n_] := If[n == 1, 1, PolyLog[-n+1, 2/3]/3];

%t rows = 10;

%t M = BellMatrix[a4123[#+1]&, rows];

%t Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 25 2019 *)

%o (Sage) # uses[bell_matrix from A264428]

%o bell_matrix(lambda n: A004123(n+1), 10) # _Peter Luschny_, Jan 18 2016

%Y Row sums are A136727.

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

%K nonn,tabl

%O 0,5

%A _Philippe Deléham_, Dec 22 2011

%E More terms from _Jean-François Alcover_, Jun 25 2019