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A184962 Triangle T(n,k), read by rows, given by (0, 1, 2, 2, 4, 3, 6, 4, 8, 5, 10, ...) DELTA (1, 0, 1, 0, 1, 0, 1, 0, ...) where DELTA is the operator defined in A084938.

%I A184962 #14 Mar 31 2016 11:30:27
%S A184962 1,0,1,0,1,1,0,3,3,1,0,13,15,6,1,0,75,95,45,10,1,0,541,735,390,105,15,
%T A184962 1,0,4683,6727,3885,1190,210,21,1,0,47293,71127,43918,14805,3010,378,
%U A184962 28,1,0,545835
%N A184962 Triangle T(n,k), read by rows, given by (0, 1, 2, 2, 4, 3, 6, 4, 8, 5, 10, ...) DELTA (1, 0, 1, 0, 1, 0, 1, 0, ...) where DELTA is the operator defined in A084938.
%C A184962 The Bell transform of the Fubini numbers. For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016
%F A184962 Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A014307(n), A000629(n) for x = 0, 1, 2 respectively.
%e A184962 Triangle begins :
%e A184962 1
%e A184962 0, 1
%e A184962 0, 1, 1
%e A184962 0, 3, 3, 1
%e A184962 0, 13, 15, 6, 1
%e A184962 0, 75, 95, 45, 10, 1
%p A184962 # The function BellMatrix is defined in A264428.
%p A184962 BellMatrix(n -> (polylog(-n,1/2)+0^n)/2, 10); # _Peter Luschny_, Jan 29 2016
%t A184962 (* The function BellMatrix is defined in A264428. *)
%t A184962 bm = BellMatrix[(PolyLog[-#, 1/2] + Boole[n == 0])/2 &, 10]; Table[bm[[n, k]], {n, 1, Length[bm]}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Mar 31 2016, after _Peter Luschny_ *)
%Y A184962 Row sums are A014307(n).
%Y A184962 Cf. A000670, A079641, A195204.
%K A184962 nonn,tabl
%O A184962 0,8
%A A184962 _Philippe Deléham_, Dec 22 2011