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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.
1
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, 1, 0, 4683, 6727, 3885, 1190, 210, 21, 1, 0, 47293, 71127, 43918, 14805, 3010, 378, 28, 1, 0, 545835
OFFSET
0,8
COMMENTS
The Bell transform of the Fubini numbers. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016
FORMULA
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A014307(n), A000629(n) for x = 0, 1, 2 respectively.
EXAMPLE
Triangle begins :
1
0, 1
0, 1, 1
0, 3, 3, 1
0, 13, 15, 6, 1
0, 75, 95, 45, 10, 1
MAPLE
# The function BellMatrix is defined in A264428.
BellMatrix(n -> (polylog(-n, 1/2)+0^n)/2, 10); # Peter Luschny, Jan 29 2016
MATHEMATICA
(* The function BellMatrix is defined in A264428. *)
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 *)
CROSSREFS
Row sums are A014307(n).
Sequence in context: A354649 A354650 A265608 * A264436 A122850 A132062
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Dec 22 2011
STATUS
approved