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A292164
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Expansion of Product_{k>=1} (1 - k^2*x^k).
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4
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1, -1, -4, -5, -7, 27, 17, 167, 110, -42, 10, -706, -4001, -3915, 3079, -18640, 9869, 21403, 130565, 107250, -15661, 420664, 599540, -161785, -1232833, -5836888, -5129796, 6516714, -29068180, -14953045, -41490510, 20261320, 30395771, 441235155, 205289550
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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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G.f.: exp(-Sum_{k>=1} Sum_{j>=1} 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; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1) +`if`(i>n, 0, i^2*b(n-i, i))))
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] = If[n == 0, 1, If[i < 1, 0,
b[n, i - 1] + If[i > n, 0, i^2*b[n - i, i]]]];
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(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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