A373691 Triangle read by rows T(n, k) is the number of permutations on n elements whose square has k descents, for n >= 1 and 0 <= k <= n-1.

1, 2, 0, 4, 2, 0, 10, 6, 6, 2, 26, 22, 48, 22, 2, 76, 68, 276, 260, 40, 0, 232, 214, 1384, 2204, 944, 62, 0, 764, 672, 6240, 16172, 13212, 3048, 200, 12, 2620, 2204, 27096, 103588, 145160, 70740, 10936, 524, 12, 9496, 7354, 113722, 612178, 1338370, 1145614, 364366, 36838, 862, 0

Offset: 1

Author

Michel Marcus, Jun 14 2024

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    2,   0;
    4,   2,    0;
   10,   6,    6,    2;
   26,  22,   48,   22,   2;
   76,  68,  276,  260,  40,  0;
  232, 214, 1384, 2204, 944, 62, 0;
  ...
		

Links

• Kassie Archer and Aaron Geary, Descents in powers of permutations, arXiv:2406.09369 [math.CO], 2024. See Table 5 p. 13.

Crossrefs

Cf. A000085 (1st column), A000142 (row sums), A037224 (right diagonal).

Cf. A003483 (square permutations), A008292.

Programs

PARI

sq(p) = vector(#p, k, p[p[k]]);
nbd(p) = sum(i=1, #p-1, p[i+1] < p[i]);
row(n) = my(v=vector(n)); for (i=1, n!, v[nbd(sq(numtoperm(n, i)))+1]++;); v;