A386880 - OEIS

A386880

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

1, 1, 6, 56, 715, 11628, 230230, 5379616, 145008513, 4431613550, 151473214816, 5727160371180, 237377895350076, 10704005376506540, 521748877569771510, 27338999059076777600, 1532576541123942256285, 91527291781199227579626, 5801648509628587739612170, 389032765009190361630625600

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

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

For n > 0, a(n) = binomial(n*(n+3)/2, n) * (n+1)/(n+3).

MATHEMATICA

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

Join[{1}, Table[Binomial[n*(n + 3)/2, n]*(n + 1)/(n + 3), {n, 1, 25}]]

CROSSREFS