A336306 a(n) = (n!)^n * [x^n] Product_{n>=1} (1 + x^k/k^n).

1, 1, 1, 35, 5392, 35462624, 15419509448256, 445352317449860352384, 1733058447330128629281872412672, 1124641798042952855847954946807366969982976, 155064212713307814902013200520441969883490549760000000000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..31

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
      b(n, i-1, k)+b(n-i, min(n-i, i-1), k)*((i-1)!*binomial(n, i))^k))
    end:
a:= n-> b(n$3):
seq(a(n), n=0..12);  # Alois P. Heinz, Jul 27 2023

Mathematica

Table[(n!)^n SeriesCoefficient[Product[(1 + x^k/k^n), {k, 1, n}], {x, 0, n}], {n, 0, 10}]

Crossrefs

Cf. A007838, A326864, A326865, A336294, A336295.

Sequence in context: A212024 A231914 A202067 * A202881 A210268 A025036

Adjacent sequences: A336303 A336304 A336305 * A336307 A336308 A336309

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 17 2020

Status

approved