A386879 - OEIS

A386879

a(n) = [x^n] 1/(1 - x)^(n*(n-1)/2).

1, 0, 1, 10, 126, 2002, 38760, 888030, 23535820, 708930508, 23930713170, 895068996640, 36749279048405, 1643385429346680, 79515468511191440, 4139207762053520646, 230672804560960311000, 13703037308872895467960, 864424422377992704918690, 57711135174726478041405270, 4065392394346039279040037520

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) ~ exp(n) * n^(n - 1/2) / (sqrt(Pi) * 2^(n + 1/2)).

For n > 0, a(n) = binomial(n*(n+1)/2, n) * (n-1)/(n+1).

MATHEMATICA

Table[SeriesCoefficient[1/(1-x)^(n*(n-1)/2), {x, 0, n}], {n, 0, 25}]

Join[{1}, Table[Binomial[n*(n+1)/2, n] * (n-1) / (n+1), {n, 1, 25}]]

CROSSREFS