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A128566
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Number of permutations of {1..n} with n inversions.
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7
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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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
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MAPLE
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a:= n-> coeff(series(mul((1-q^j)/(1-q), j=1..n), q, n+1), q, n):
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MATHEMATICA
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Table[SeriesCoefficient[QPochhammer[x, x, n]/(1-x)^n, {x, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, May 13 2016 *)
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PROG
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(PARI) {a(n)=polcoeff(prod(j=1, n, (1-q^j)/(1-q)), n, q)}
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CROSSREFS
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Diagonal of A008302 (Mahonian numbers).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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