A137855 Triangle read by rows: T(n,k) = Sum_{j=1..n-k+1} Stirling2(k, j).

1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 5, 8, 1, 1, 2, 5, 14, 16, 1, 1, 2, 5, 15, 41, 32, 1, 1, 2, 5, 15, 51, 122, 64, 1, 1, 2, 5, 15, 52, 187, 365, 128, 1, 1, 2, 5, 15, 52, 202, 715, 1094, 256, 1, 1, 2, 5, 15, 52, 203, 855, 2795, 3281, 512, 1

Offset

1,5

Comments

Rows of the array tend to A000110 starting (1, 2, 5, 15, 52, ...).

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275

Formula

Take antidiagonals of an array formed by A000012 * A008277(transform), where A000012 = (1; 1,1; 1,1,1; ...) and A008277 = the Stirling2 triangle.

Example

First few rows of the array:
  1, 1, 1,  1,  1, ...
  1, 2, 4,  8, 16, ...
  1, 2, 5, 14, 41, ...
  1, 2, 5, 14, 51, ...
  1, 2, 5, 14, 52, ...
  ...
First few rows of the triangle:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 4,  1;
  1, 2, 5,  8,  1;
  1, 2, 5, 14, 16,   1;
  1, 2, 5, 15, 41,  32,   1;
  1, 2, 5, 15, 51, 122,  64,    1;
  1, 2, 5, 15, 52, 187, 365,  128,   1;
  1, 2, 5, 15, 52, 202, 715, 1094, 256, 1;
  ...

Prog

(PARI) T(n, k)={sum(j=1, n-k+1, stirling(k, j, 2))} \\ Andrew Howroyd, Aug 09 2018

Crossrefs

Row sums are A137856.

Cf. A008277, A000110, A203647, A278984.

Sequence in context: A027935 A137940 A274859 * A113143 A181802 A110971

Adjacent sequences: A137852 A137853 A137854 * A137856 A137857 A137858

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 16 2008

Extensions

Name changed by Andrew Howroyd, Aug 09 2018

Status

approved