A067924 - OEIS

A067924

Triangle read by rows in which the n-th 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) terms on each row, where p(n) = A000041(n).

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 terms in row n 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 [math.CO], 2015-2016.

EXAMPLE