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A128566 Number of permutations of {1..n} with n inversions. 7
1, 0, 0, 1, 5, 22, 90, 359, 1415, 5545, 21670, 84591, 330121, 1288587, 5032235, 19664205, 76893687, 300895513, 1178290263, 4617369760, 18106447251, 71048746505, 278966179936, 1095987764828, 4308300939450, 16944940572831, 66680029591816, 262519664110588 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

a(n) = A008302(n,n) = coefficient of q^n in the q-factorial of n.

a(n) = T(n,n) with T(n,k) = T(n-1,k) + Sum_{j=1..n-1} T(n-1,k-j) for n>=0, k>0; T(n,k) = 0 for n<0; T(n,0) = 1 for n>=0. - Alois P. Heinz, Mar 07 2013

a(n) ~ c * 2^(2*n-1) / sqrt(Pi*n), where c = A048651 = QPochhammer[1/2] = 0.28878809508660242127889972192923... . - Vaclav Kotesovec, Sep 07 2014

MAPLE

a:= n-> coeff(series(mul((1-q^j)/(1-q), j=1..n), q, n+1), q, n):

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 05 2013

MATHEMATICA

Table[SeriesCoefficient[QPochhammer[x, x, n]/(1-x)^n, {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, May 13 2016 *)

PROG

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

CROSSREFS

Diagonal of A008302 (Mahonian numbers).

Column 2 of A128564.

Cf. A128565 (column 1), A214086, A048651.

Sequence in context: A037529 A108072 A081892 * A097138 A208736 A050185

Adjacent sequences:  A128563 A128564 A128565 * A128567 A128568 A128569

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 12 2007

EXTENSIONS

Edited by Alois P. Heinz, Mar 05 2013

STATUS

approved

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Last modified February 21 23:44 EST 2019. Contains 320381 sequences. (Running on oeis4.)