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

0,4

Links

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

Example

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

Maple

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

Mathematica

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

Crossrefs

Cf. A007838, A249588, A326865.

Cf. A087132.

Sequence in context: A196928 A266002 A367554 * A083341 A336347 A075604

Adjacent sequences: A326861 A326862 A326863 * A326865 A326866 A326867

Keyword

nonn

Author

Vaclav Kotesovec, Jul 27 2019

Status

approved