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

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

A059797 begins 2, 5, 5, 9, 16, 9, so row six of this sequence begins 1, 5, 10, 10, 5, 1, 9, 16, 9, ...
Triangle begins:
  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