A137596 Triangle read by rows: T(n, k) = Sum_{i=0..n) Stirling2(i, k).

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 11, 7, 1, 1, 5, 26, 32, 11, 1, 1, 6, 57, 122, 76, 16, 1, 1, 7, 120, 423, 426, 156, 22, 1, 1, 8, 247, 1389, 2127, 1206, 288, 29, 1, 1, 9, 502, 4414, 9897, 8157, 2934, 491, 37, 1

Offset

0,5

Links

Table of n, a(n) for n=0..54.

Formula

T = A000012 * A048993 as infinite lower triangular matrices.

T(n, k) = Sum_{i=0..n-k} Stirling2(i+k, k). - Igor Victorovich Statsenko, May 25 2024

Example

First few rows of the triangle:
  1;
  1, 1;
  1, 2,   1;
  1, 3,   4,   1;
  1, 4,  11,   7,   1;
  1, 5,  26,  32,  11,   1;
  1, 6,  57, 122,  76,  16,  1;
  1, 7, 120, 423, 426, 156, 22, 1;
  ...

Maple

T := (n, k) -> add(Stirling2(i, k), i=0..n):
seq(seq(T(n, k), k=0..n), n=0..9);  # Peter Luschny, Mar 07 2025

Crossrefs

Cf. A005001 (row sums), A048993.

Sequence in context: A340814 A063841 A256161 * A111669 A336573 A124834

Adjacent sequences: A137593 A137594 A137595 * A137597 A137598 A137599

Keyword

nonn,tabl,changed

Author

Gary W. Adamson, Jan 29 2008

Extensions

Offset set to 0 by Peter Luschny, May 25 2024

Status

approved