%I #13 Jul 27 2023 16:33:24
%S 1,1,1,13,100,1876,57636,2051316,104640768,6819033600,576652089600,
%T 57187381536000,7057192160793600,1014733052692300800,
%U 172646881540527744000,33848454886497227289600,7637231669166956976537600,1948418678155880277481881600
%N G.f.: Product_{k>=1} (1 + x^k/k^2) = Sum_{n>=0} a(n)*x^n/n!^2.
%H Alois P. Heinz, <a href="/A326864/b326864.txt">Table of n, a(n) for n = 0..254</a>
%e a(n) ~ c * (n-1)!^2, where c = A156648 = Product_{k>=1} (1 + 1/k^2) = sinh(Pi)/Pi = 3.67607791037497772...
%p b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
%p b(n, i-1)+b(n-i, min(n-i, i-1))*((i-1)!*binomial(n, i))^2))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jul 27 2023
%t nmax = 20; CoefficientList[Series[Product[(1+x^k/k^2), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!^2
%Y Cf. A007838, A249588, A326865.
%Y Cf. A087132.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Jul 27 2019
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