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, 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

Author

Philippe Deléham, Dec 22 2011

Keywords

• nonn
• tabl

Comments

The Bell transform of the Fubini numbers. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

Examples

			Triangle begins :
1
0, 1
0, 1, 1
0, 3, 3, 1
0, 13, 15, 6, 1
0, 75, 95, 45, 10, 1
		

Crossrefs

Row sums are A014307(n).

Cf. A000670, A079641, A195204.

Programs

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 *)

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A014307(n), A000629(n) for x = 0, 1, 2 respectively.