A128565 Column 1 of triangle A128564; a(n) equals the number of permutations of {1..n+2} with [n/2+1] inversions for n>=0.

1, 2, 5, 9, 29, 49, 174, 285, 1068, 1717, 6655, 10569, 41926, 66013, 266338, 416687, 1703027, 2651355, 10947079, 16976806, 70673825, 109256095, 457927079, 706071989, 2976282415, 4579020513, 19395654894, 29784426945, 126688273871, 194231327451, 829176461458

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = A008302(n+2,[n/2+1]) = coefficient of q^[n/2+1] in the q-factorial of n+2 for n>=0.

Prog

(PARI) {a(n)=polcoeff(prod(j=1, n+2, (1-q^j)/(1-q)), (n+2)\2, q)}

Crossrefs

Cf. A008302 (Mahonian numbers); A128564 (triangle), A128566 (column 2).

Sequence in context: A086586 A105456 A364797 * A366505 A359386 A151952

Adjacent sequences: A128562 A128563 A128564 * A128566 A128567 A128568

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2007

Status

approved