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A326864
G.f.: Product_{k>=1} (1 + x^k/k^2) = Sum_{n>=0} a(n)*x^n/n!^2.
5
1, 1, 1, 13, 100, 1876, 57636, 2051316, 104640768, 6819033600, 576652089600, 57187381536000, 7057192160793600, 1014733052692300800, 172646881540527744000, 33848454886497227289600, 7637231669166956976537600, 1948418678155880277481881600
OFFSET
0,4
LINKS
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 27 2019
STATUS
approved