A291968 Triangle read by rows: T(n,k) = (k+1) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

1, 0, 2, 0, 2, 0, 2, 6, 0, 2, 6, 0, 2, 12, 0, 2, 12, 24, 0, 2, 18, 24, 0, 2, 18, 48, 0, 2, 24, 72, 0, 2, 24, 96, 120, 0, 2, 30, 120, 120, 0, 2, 30, 168, 240, 0, 2, 36, 192, 360, 0, 2, 36, 240, 600, 0, 2, 42, 288, 720, 720, 0, 2, 42, 336, 1080, 720, 0, 2, 48, 384

Offset

0,3

Links

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

Formula

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

Example

First few rows are:
  1;
  0, 2;
  0, 2;
  0, 2,  6;
  0, 2,  6;
  0, 2, 12;
  0, 2, 12, 24;
  0, 2, 18, 24;
  0, 2, 18, 48;
  0, 2, 24, 72;
  0, 2, 24, 96, 120.

Crossrefs

Row sums give A072576.

Columns 0-1 give A000007, A007395.

Cf. A216652.

Sequence in context: A291970 A281981 A159006 * A226171 A284280 A278520

Adjacent sequences: A291965 A291966 A291967 * A291969 A291970 A291971

Keyword

nonn,tabf

Author

Seiichi Manyama, Sep 07 2017

Status

approved