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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).

%I A067924 #16 Aug 30 2023 07:27:49
%S A067924 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,
%T A067924 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,
%U A067924 28,70,56,56,70,28,14,42,14
%N 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).
%C A067924 These are Betti numbers [Dochtermann]. - _N. J. A. Sloane_, Dec 02 2015
%C A067924 Number of terms in row n is A000041(n).
%C A067924 Row sums generate sequence A000085: 1, 2, 4, 10, 26, 76, ...
%C A067924 Sum of squares generates A000142; e.g., -1*1 + 4*4 + 6*6 + 4*4 + 1*1 + 5*5 +5*5 = 5! = 120.
%H A067924 A. Dochtermann, <a href="http://arxiv.org/abs/1503.06243">Face rings of cycles, associahedra, and standard Young tableaux</a>, arXiv preprint arXiv:1503.06243 [math.CO], 2015-2016.
%e A067924 A059797 begins 2, 5, 5, 9, 16, 9, so row six of this sequence begins 1, 5, 10, 10, 5, 1, 9, 16, 9, ...
%e A067924 Triangle begins:
%e A067924   1;
%e A067924   1, 1;
%e A067924   1, 2,  1;
%e A067924   1, 3,  3,  1,  2;
%e A067924   1, 4,  6,  4,  1,  5, 5;
%e A067924   1, 5, 10, 10,  5,  1, 9, 16,  9,  5,  5;
%e A067924   1, 6, 15, 20, 15,  6, 1, 14, 35, 35, 14, 14, 21, 21, 14;
%e A067924   1, 7, 21, 35, 35, 21, 7,  1, 20, 64, 90, 64, 20, 28, 70, 56, 56, 70, 28, 14, 42, 14;
%Y A067924 Cf. A000041, A000085, A000142, A059797, A060240.
%K A067924 nice,nonn,tabf
%O A067924 1,5
%A A067924 _Alford Arnold_, Mar 04 2002