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A239165
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Number of partitions of 6^n into parts that are at most n with at least one part of each size.
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2
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0, 1, 17, 3781, 14942231, 1264608203048, 2555847904495965819, 132574244496779071303074376, 185560862224740635595130202984468935, 7271076505438083132065943012753686950455454055, 8205115354631567886718289443554629632451344416164686337673
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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) = [x^(6^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).
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MATHEMATICA
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maxExponent = 50; a[0] = 0; a[1] = 1;
a[n_] := Module[{}, aparts = List @@ (Product[1/(1 - x^j), {j, 1, n}] // Apart); cc = aparts + O[x]^maxExponent // CoefficientList[#, x]&; f[k_] = Total[FindSequenceFunction[#, k]& /@ cc]; f[6^n-n(n+1)/2+1] // Round];
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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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