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%I #14 Mar 31 2016 11:30:27
%S 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 1,0,4683,6727,3885,1190,210,21,1,0,47293,71127,43918,14805,3010,378,
%U 28,1,0,545835
%N 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 The Bell transform of the Fubini numbers. For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016
%F Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A014307(n), A000629(n) for x = 0, 1, 2 respectively.
%e Triangle begins :
%e 1
%e 0, 1
%e 0, 1, 1
%e 0, 3, 3, 1
%e 0, 13, 15, 6, 1
%e 0, 75, 95, 45, 10, 1
%p # The function BellMatrix is defined in A264428.
%p BellMatrix(n -> (polylog(-n,1/2)+0^n)/2, 10); # _Peter Luschny_, Jan 29 2016
%t (* The function BellMatrix is defined in A264428. *)
%t 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 Row sums are A014307(n).
%Y Cf. A000670, A079641, A195204.
%K nonn,tabl
%O 0,8
%A _Philippe Deléham_, Dec 22 2011
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