A205574 Triangle T(n,k), 0<=k<=n, given by (0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 5, 3, 1, 0, 15, 14, 9, 4, 1, 0, 52, 44, 28, 14, 5, 1, 0, 203, 154, 93, 48, 20, 6, 1, 0, 877, 595, 333, 169, 75, 27, 7, 1, 0, 4140, 2518, 1289, 624, 280, 110, 35, 8, 1, 0, 21147, 11591, 5394, 2442, 1071, 435, 154, 44, 9, 1

Offset

0,8

Comments

Bell convolution triangle ; g.f. for column k : (x*B(x))^k with B(x) g.f. for A000110 (Bell numbers).

Riordan array (1, x*B(x)), when B(x) the g.f. of A000110.

Row sums are in A137551.

Links

Alois P. Heinz, Rows n = 0..140, flattened

Formula

Sum_{k=0..n} T(n,k) = A137551(n), n>0.

Example

Triangle begins:
  1;
  0,   1;
  0,   1,   1;
  0,   2,   2,  1;
  0,   5,   5,  3,  1;
  0,  15,  14,  9,  4,  1;
  0,  52,  44, 28, 14,  5, 1;
  0, 203, 154, 93, 48, 20, 6, 1;
  ...

Maple

# Uses function PMatrix from A357368.
PMatrix(10, n -> combinat:-bell(n-1)); # Peter Luschny, Oct 19 2022

Crossrefs

Cf. Columns : A000007, A000110, A014322, A014323, A014325 ; Diagonals : A000012, A001477, A000096, A005586.

Another version: A292870.

T(2n,n) gives: A292871.

Sequence in context: A059365 A106566 A099039 * A049244 A110281 A120059

Adjacent sequences: A205571 A205572 A205573 * A205575 A205576 A205577

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Jan 29 2012

Status

approved