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A111933
Triangle read by rows, generated from Stirling cycle numbers.
3
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
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
Column 3 of the array = A005449.
Column 4 of the array = A094952.
Sequence in context: A330141 A007441 A289192 * A144304 A122941 A297622
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