A111933 Triangle read by rows, generated from Stirling cycle numbers.

1, 1, 1, 1, 2, 2, 1, 3, 7, 6, 1, 4, 15, 35, 24, 1, 5, 26, 105, 228, 120, 1, 6, 40, 234, 947, 1834, 720, 1, 7, 57, 440, 2696, 10472, 17582, 5040, 1, 8, 77, 741, 6170, 37919, 137337, 195866, 40320, 1, 9, 100, 1155, 12244, 105315, 630521, 2085605, 2487832, 362880

Offset: 1

Author

Gary W. Adamson, Aug 21 2005

Keywords

• nonn
• tabl

Comments

Let M = the infinite lower triangular matrix of Stirling cycle numbers (A008275). Perform M^n * [1, 0, 0, 0, ...] forming an array. Antidiagonals of that array become the rows of this triangle.

Examples

			Row 5 of the triangle = 1, 4, 15, 35, 24; generated from M^n * [1,0,0,0,...] (n = 1 through 5); then take antidiagonals.
Terms in the array, first few rows are:
  1, 1,  2,   6,    24,    120, ...
  1, 2,  7,  35,   228,   1834, ...
  1, 3, 15, 105,   947,  10472, ...
  1, 4, 26, 234,  2697,  37919, ...
  1, 5, 40, 440,  6170, 105315, ...
  1, 6, 57, 741, 12244, 245755, ...
  ...
First few rows of the triangle are:
  1;
  1, 1;
  1, 2,  2;
  1, 3,  7,   6;
  1, 4, 15,  35,  24;
  1, 5, 26, 105, 228,  120;
  1, 6, 40, 234, 947, 1834, 720;
  ...
		

Links

• Seiichi Manyama, Antidiagonals n = 1..140, flattened

Crossrefs

Row 1..7 give A000142(n-1), A003713, A000268, A000310, A000359, A000406, A001765.

Column 3 of the array = A005449.

Column 4 of the array = A094952.

Cf. A008275, A302358.

Extensions

a(28), a(36) and a(45) corrected by Seiichi Manyama, Feb 11 2022