A326865 -id:A326865 - cp's OEIS frontend

A326864 G.f.: Product_{k>=1} (1 + x^k/k^2) = Sum_{n>=0} a(n)*x^n/n!^2.

1, 1, 1, 13, 100, 1876, 57636, 2051316, 104640768, 6819033600, 576652089600, 57187381536000, 7057192160793600, 1014733052692300800, 172646881540527744000, 33848454886497227289600, 7637231669166956976537600, 1948418678155880277481881600

Offset: 0

Vaclav Kotesovec, Jul 27 2019

nonn

			a(n) ~ c * (n-1)!^2, where c = A156648 = Product_{k>=1} (1 + 1/k^2) = sinh(Pi)/Pi = 3.67607791037497772...

Alois P. Heinz, Table of n, a(n) for n = 0..254

Cf. A007838, A249588, A326865.

Cf. A087132.

b:= proc(n, i) option remember; `if`(i*(i+1)/2 b(n$2):
seq(a(n), n=0..20);  # Alois P. Heinz, Jul 27 2023

nmax = 20; CoefficientList[Series[Product[(1+x^k/k^2), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!^2

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

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Jul 17 2020

nonn

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

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

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

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

cp's OEIS Frontend

A326864 G.f.: Product_{k>=1} (1 + x^k/k^2) = Sum_{n>=0} a(n)*x^n/n!^2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica