

A067924


Triangle T(n,k) in which nth row gives degrees of irreducible representations of symmetric group S_n. (cf. A060240) but now rows are sorted as indicated in A059797 with p(n) entries on each row, where p(n) = A000041(n).


2



1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 1, 4, 6, 4, 1, 5, 5, 1, 5, 10, 10, 5, 1, 9, 16, 9, 5, 5, 1, 6, 15, 20, 15, 6, 1, 14, 35, 35, 14, 14, 21, 21, 14, 1, 7, 21, 35, 35, 21, 7, 1, 20, 64, 90, 64, 20, 28, 70, 56, 56, 70, 28, 14, 42, 14
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OFFSET

1,5


COMMENTS

These are Betti numbers [Dochtermann].  N. J. A. Sloane, Dec 02 2015
Number of entries on each row is A000041(n).
Row sums generate sequence A000085: 1 2 4 10 26 76 ...
Sum of squares generates A000142 e.g.  1*1 + 4*4 + 6*6 +4*4 + 1*1 + 5*5 +5*5 = 5! = 120


LINKS

Table of n, a(n) for n=1..66.
A. Dochtermann, Face rings of cycles, associahedra, and standard Young tableaux, arXiv preprint arXiv:1503.06243, 2015


EXAMPLE

A059797 begins 2 5 5 9 16 9 so row six of this sequence begins 1 5 10 10 5 1 9 16 9 ...
1;
1, 1;
1, 2, 1;
1, 3, 3, 1, 2;
1, 4, 6, 4, 1, 5, 5;
1, 5, 10, 10, 5, 1, 9, 16, 9, 5, 5;
1, 6, 15, 20, 15, 6, 1, 14, 35, 35, 14, 14, 21, 21, 14;
1, 7, 21, 35, 35, 21, 7, 1, 20, 64, 90, 64, 20, 28, 70, 56, 56, 70, 28, 14, 42, 14;


CROSSREFS

Cf. A000041, A000085, A000142, A059797, A060240.
Sequence in context: A129453 A129455 A329322 * A344912 A056670 A170925
Adjacent sequences: A067921 A067922 A067923 * A067925 A067926 A067927


KEYWORD

nice,nonn,tabf


AUTHOR

Alford Arnold, Mar 04 2002


STATUS

approved



