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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.

%I A185285 #21 Mar 28 2020 14:02:49
%S A185285 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 A185285 2430,380,30,1,0,133210,119574,42070,7630,770,42,1,0,2299754,2170252,
%U A185285 822696,166320,19740,1400,56,1,0,45375130,44657106,17985268,3956568,528780,44604,2352,72,1
%N 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.
%C A185285 The Bell transform of A004123(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 18 2016
%e A185285 Triangle begins :
%e A185285 1
%e A185285 0, 1
%e A185285 0, 2, 1
%e A185285 0, 10, 6, 1
%e A185285 0, 74, 52, 12, 1
%e A185285 0, 730, 570, 160, 20, 1
%e A185285 0, 9002, 7600, 2430, 380, 30, 1
%e A185285 0, 133210, 119574, 42070, 7630, 770, 42, 1
%t A185285 (* The function BellMatrix is defined in A264428. *)
%t A185285 a4123[n_] := If[n == 1, 1, PolyLog[-n+1, 2/3]/3];
%t A185285 rows = 10;
%t A185285 M = BellMatrix[a4123[#+1]&, rows];
%t A185285 Table[M[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 25 2019 *)
%o A185285 (Sage) # uses[bell_matrix from A264428]
%o A185285 bell_matrix(lambda n: A004123(n+1), 10) # _Peter Luschny_, Jan 18 2016
%Y A185285 Row sums are A136727.
%Y A185285 Cf. A000007, A004123, A000012, A002378, A195205.
%K A185285 nonn,tabl
%O A185285 0,5
%A A185285 _Philippe Deléham_, Dec 22 2011
%E A185285 More terms from _Jean-François Alcover_, Jun 25 2019