OFFSET
0,9
LINKS
Toufik Mansour, Howard Skogman, and Rebecca Smith, Sorting inversion sequences, arXiv:2401.06662 [math.CO], 2024. See Theorem 3.25 at page 13.
FORMULA
G.f.: ((1 - x)(1 - 2*x) - ((1 - x)*(1 - 2*x) + x^2)*y)/((1 - x)*(1 - 2*x) - (1 - x)*(2 - 3*x)*y + (1 - 2*x)*y^2).
EXAMPLE
The array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 1, 4, 9, 16, 25, ...
0, 1, 8, 24, 52, 95, ...
0, 1, 16, 59, 149, 310, ...
0, 1, 32, 138, 396, 923, ...
...
MATHEMATICA
A[n_, k_]:=SeriesCoefficient[((1-x)(1-2x)-((1-x)(1-2x)+x^2)y)/((1-x)(1-2x)-(1-x)(2-3x)y+(1-2x)y^2), {x, 0, n}, {y, 0, k}]; Table[A[n-k, k], {n, 0, 11}, {k, 0, n}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Jan 20 2024
STATUS
approved