A108469 Main diagonal of A090806.

1, 1, 2, 4, 9, 20, 45, 100, 220, 478, 1025, 2169, 4534, 9364, 19125, 38646, 77306, 153173, 300765, 585518, 1130612, 2166284, 4120062, 7780817, 14595364, 27201794, 50383690, 92768457, 169835952, 309223286, 560036477, 1009124256

Offset: 0

Author

Christian G. Bower, Jun 03 2005

Keywords

• nonn

References

• Alter, Ronald; Curtz, Thaddeus B.; Wang, Chung C. Permutations with fixed index and number of inversions. Proceedings of the Fifth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1974), pp. 209-228. Congressus Numerantium, No. X, Utilitas Math., Winnipeg, Man., 1974.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..90

Programs

Mathematica

nmax = 20; p = 1; Do[Do[p = Expand[p*(1 - x^i*y^j)]; p = Select[p, (Exponent[#, x] <= nmax) && (Exponent[#, y] <= nmax) &], {i, 1, nmax}], {j, 1, nmax}]; p = Expand[Normal[Series[1/p, {x, 0, nmax}, {y, 0, nmax}]]]; p = Select[p, Exponent[#, x] == Exponent[#, y] &]; Flatten[{1, Table[Coefficient[p, x^n*y^n], {n, 1, nmax}]}] (* Vaclav Kotesovec, Apr 08 2016 *)