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A292165
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Expansion of Product_{k>=1} 1/(1 + k^2*x^k).
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3
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1, -1, -3, -6, 6, 5, 40, 11, 226, -516, -186, -844, 3731, -3734, 814, -33819, 85660, -46022, 210342, -411678, 593996, -2980156, 2076721, -3445584, 40785410, -37503158, 98085, -271846888, 336918770, -295108832, 2178341296, -2404059340, 6127604258
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ (-1)^n * c * 3^(2*n/3), where
c = 0.717271758899891528435966115495396784611147877234945... if mod(n,3)=0
c = 0.387695187106751505296020614217498222070185848125472... if mod(n,3)=1
c = 0.241939482775588594057384356004734639024152664456553... if mod(n,3)=2
(End)
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*j^(2*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 18 2018
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MAPLE
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b:= proc(n, i) option remember; (m->
`if`(m<n, 0, `if`(n=m, i!^2, b(n, i-1)+
`if`(i>n, 0, i^2*b(n-i, i-1)))))(i*(i+1)/2)
end:
a:= proc(n) option remember; `if`(n=0, 1,
-add(b(n-i$2)*a(i$2), i=0..n-1))
end:
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MATHEMATICA
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b[n_, i_] := b[n, i] = Function[m,
If[m < n, 0, If[n == m, i!^2, b[n, i - 1] +
If[i > n, 0, i^2*b[n - i, i - 1]]]]][i*(i + 1)/2];
a[n_] := a[n] = If[n == 0, 1, -Sum[b[n - i, n - i]*a[i], {i, 0, n - 1}]];
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(1/prod(n=1, N, 1+n^2*x^n))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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