A111933 - OEIS

%I #36 Feb 13 2022 23:16:43

%S 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,

%T 1834,720,1,7,57,440,2696,10472,17582,5040,1,8,77,741,6170,37919,

%U 137337,195866,40320,1,9,100,1155,12244,105315,630521,2085605,2487832,362880

%N Triangle read by rows, generated from Stirling cycle numbers.

%C 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.

%H Seiichi Manyama, <a href="/A111933/b111933.txt">Antidiagonals n = 1..140, flattened</a>

%e 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.

%e Terms in the array, first few rows are:

%e   1, 1,  2,   6,    24,    120, ...

%e   1, 2,  7,  35,   228,   1834, ...

%e   1, 3, 15, 105,   947,  10472, ...

%e   1, 4, 26, 234,  2697,  37919, ...

%e   1, 5, 40, 440,  6170, 105315, ...

%e   1, 6, 57, 741, 12244, 245755, ...

%e   ...

%e First few rows of the triangle are:

%e   1;

%e   1, 1;

%e   1, 2,  2;

%e   1, 3,  7,   6;

%e   1, 4, 15,  35,  24;

%e   1, 5, 26, 105, 228,  120;

%e   1, 6, 40, 234, 947, 1834, 720;

%e   ...

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

%Y Column 3 of the array = A005449.

%Y Column 4 of the array = A094952.

%Y Cf. A008275, A302358.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Aug 21 2005

%E a(28), a(36) and a(45) corrected by _Seiichi Manyama_, Feb 11 2022