A291969 Triangle read by rows: T(n,k) = k * (T(n-k,k-1) + T(n-k,k)) with T(0,0) = 1 for 0 <= k <= A003056(n).

1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 6, 0, 1, 6, 6, 0, 1, 14, 6, 0, 1, 14, 18, 0, 1, 30, 36, 0, 1, 30, 60, 24, 0, 1, 62, 96, 24, 0, 1, 62, 198, 72, 0, 1, 126, 270, 144, 0, 1, 126, 474, 336, 0, 1, 254, 780, 480, 120, 0, 1, 254, 1188, 1080, 120, 0, 1, 510, 1800

Offset

0,8

Links

Seiichi Manyama, Rows n = 0..481, flattened

Formula

G.f. of column k: k! * x^(k*(k+1)/2) / Product_{j=1..k} (1-j*x^j).

Example

First few rows are:
  1;
  0, 1;
  0, 1;
  0, 1,  2;
  0, 1,  2;
  0, 1,  6;
  0, 1,  6,  6;
  0, 1, 14,  6;
  0, 1, 14, 18;
  0, 1, 30, 36;
  0, 1, 30, 60, 24.

Crossrefs

Row sums give A204858.

Columns 0-1 give A000007, A000012.

Cf. A291960.

Sequence in context: A029300 A096397 A337547 * A321434 A103919 A263234

Adjacent sequences: A291966 A291967 A291968 * A291970 A291971 A291972

Keyword

nonn,tabf

Author

Seiichi Manyama, Sep 07 2017

Status

approved