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

1,5

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.

Links

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

Example

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;
  ...

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.

Sequence in context: A330141 A007441 A289192 * A144304 A122941 A297622

Adjacent sequences: A111930 A111931 A111932 * A111934 A111935 A111936

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 21 2005

Extensions

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

Status

approved