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A239162
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Number of partitions of 3^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, 4, 48, 3042, 1067474, 2215932130, 29012104252380, 2526293243761311036, 1525710603023191548743988, 6600334932211428773703751221040, 209705652574790086852527310591449309624, 49907101066058865036206450041083799915221352487
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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^(3^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).
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EXAMPLE
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a(2) = 4: 22221, 222111, 2211111, 21111111.
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MATHEMATICA
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maxExponent = 30; 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[3^n - n(n+1)/2 + 1] // Round]; Table[an = a[n];
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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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