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A206227
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Number of partitions of n^2+n into parts not greater than n.
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4
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1, 1, 4, 19, 108, 674, 4494, 31275, 225132, 1662894, 12541802, 96225037, 748935563, 5900502806, 46976736513, 377425326138, 3056671009814, 24930725879856, 204623068332997, 1688980598900228, 14012122025369431, 116784468316023069, 977437078888272796, 8212186058546599006
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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^(n^2+n)] Product_{k=1..n} 1/(1 - x^k).
a(n) ~ c * d^n / n^2, where d = 9.1533701924541224619485302924013545... = A258268, c = 0.3572966225745094270279188015952797... . - Vaclav Kotesovec, Sep 07 2014
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MAPLE
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T:= proc(n, k) option remember;
`if`(n=0 or k=1, 1, T(n, k-1) + `if`(k>n, 0, T(n-k, k)))
end:
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MATHEMATICA
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Table[SeriesCoefficient[Product[1/(1-x^k), {k, 1, n}], {x, 0, n*(n+1)}], {n, 0, 20}] (* Vaclav Kotesovec, May 25 2015 *)
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PROG
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(PARI) {a(n)=polcoeff(prod(k=1, n, 1/(1-x^k+x*O(x^(n^2+n)))), n^2+n)}
for(n=0, 30, print1(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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