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

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