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A023879
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Number of partitions in expanding space.
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6
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1, 1, 3, 12, 79, 722, 8675, 128177, 2248873, 45644104, 1051632553, 27107038863, 772751427746, 24136897360750, 819689757351091, 30068876227952332, 1184869328943005936, 49914047187427191742
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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.: Product_{k>=1} (1 - x^k)^(-k^(k-1)).
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MAPLE
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seq(coeff(series(mul((1-x^k)^(-k^(k-1)), k=1..n), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 31 2018
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MATHEMATICA
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nmax=20; CoefficientList[Series[Product[1/(1-x^k)^(k^(k-1)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)
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PROG
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(PARI) {a(n)=polcoeff(prod(k=1, n, (1-x^k+x*O(x^n))^(-k^(k-1))), n)}
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, sumdiv(m, d, d^d)*x^m/m) +x*O(x^n)), n)} \\ Paul D. Hanna, Sep 05 2012
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^(k^(k-1)): k in [1..m]]) )); // G. C. Greubel, Oct 31 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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