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

Offset: 0

Author

Vaclav Kotesovec, Aug 06 2025

Keywords

• nonn

Crossrefs

Cf. A014068, A054688, A116508, A177234, A386880.

Programs

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}]]

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).