A164341 -id:A164341 - cp's OEIS frontend

A164342 Row sums of table A164341.

1, 4, 9, 27, 61, 185, 469, 1456, 4368, 14720, 50800, 190149, 735451, 3001161, 12659652, 55462967, 250186665, 1163114375, 5548002866, 27151477487, 135968479892, 696511087808, 3643182769117, 19449907766921, 105843172596610

Offset: 1

Wouter Meeussen, Aug 13 2009

nonn

T. Kyle Petersen and Bridget Eileen Tenner, How to write a permutation as a product of involutions (and why you might care), arXiv:1202.5319, 2012

Cf. A164341.

A173869 Irregular table T(n,k) = A164341(n,k) * A036039(n,k) read by rows.

Original entry on oeis.org

1, 2, 2, 6, 6, 4, 24, 24, 18, 24, 10, 120, 120, 120, 120, 90, 80, 26, 720, 720, 720, 480, 720, 720, 300, 480, 540, 300, 76, 5040, 5040, 5040, 5040, 5040, 5040, 3360, 3780, 3360, 5040, 2100, 2100, 2520, 1092, 232, 40320, 40320, 40320, 40320, 25200, 40320

Offset: 1

Alford Arnold, Mar 12 2010

The n-th row has A000041(n) columns.
The row sums yield A111883(n) = A000085(n)^2.
A000041 and A000085 are also relevant to the table defined by A104778.

			The row lengths of A164341 and A036039 are the same, so one can multiply
the flattened arrays point-by-point to compute this sequence here:
1..2..2..3..2..4.. A164341 times
1..1..1..2..3..1.. A036039 yields
1..2..2..6..6..4..

Cf. A000041, A000085, A036039, A104778, A111883, A164341.

Definition rephrased by R. J. Mathar, Mar 26 2010

A214430 Triangle read by rows, where T(n,m) is sum of the absolute values of the m-th column (in lexicographic ordering) in the character table of S_n.

Original entry on oeis.org

1, 2, 2, 4, 2, 3, 10, 4, 6, 3, 4, 26, 8, 6, 6, 6, 4, 5, 76, 20, 12, 20, 12, 6, 12, 8, 8, 5, 6, 232, 52, 24, 20, 30, 12, 18, 12, 16, 8, 12, 10, 10, 6, 7, 764, 148, 52, 36, 76, 78, 24, 18, 24, 24, 36, 12, 20, 12, 20, 20, 10, 15, 12, 12, 7, 8, 2620, 460, 148, 76, 76, 208, 56, 32, 56, 40, 24, 54, 100, 28, 20, 20, 20, 20, 50

Offset: 1

Kyle Petersen, Jul 17 2012

Ordering on partitions is lexicographic, where partitions themselves are written in decreasing order, e.g., for n=5, the order is [1,1,1,1,1] < [2,1,1,1] < [2,2,1] < [3,1,1] < [3,2] < [4,1] < [5].

			The character table for S_3 is / 1 1 1 / 2 0 -1 / 1 -1 1 / and so T(3,1)=4, T(3,2)=2, and T(3,3)=3.
Displayed as a triangle:
1
2, 2
4, 2, 3
10, 4, 6, 3, 4
26, 8, 6, 6, 6, 4, 5
76, 20, 12, 20, 12, 6, 12, 8, 8, 5, 6
232, 52, 24, 20, 30, 12, 18, 12, 16, 8, 12, 10, 10, 6, 7
764, 148, 52, 36, 76, 78, 24, 18, 24, 24, 36, 12, 20, 12, 20, 20, 10, 15, 12, 12, 7, 8

Kyle Petersen, Table of n, a(n) for n = 1..138
T. Kyle Petersen and Bridget Eileen Tenner, How to write a permutation as a product of involutions (and why you might care), arXiv:1202.5319 [math.CO], 2012.

Equal to A164341 for n<=7, row sums given in A214418. First column, corresponding to partition [1,1,...,1], is given by A000085.

#For row n, we have the following.
P:=combinat[partition](n):
seq(add(abs(combinat[Chi](l, m)), l in P), m in P);

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A164342 Row sums of table A164341.

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A173869 Irregular table T(n,k) = A164341(n,k) * A036039(n,k) read by rows.

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A214430 Triangle read by rows, where T(n,m) is sum of the absolute values of the m-th column (in lexicographic ordering) in the character table of S_n.

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