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

0,8

Comments

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

Links

Table of n, a(n) for n=0..46.

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).

Cf. A000670, A079641, A195204.

Sequence in context: A354649 A354650 A265608 * A264436 A122850 A132062

Adjacent sequences: A184959 A184960 A184961 * A184963 A184964 A184965

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 22 2011

Status

approved