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A203156
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(n-1)-st elementary symmetric function of {4,9,16,25,..., (n+1)^2}.
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1
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1, 13, 244, 6676, 254736, 13000464, 857431296, 71077637376, 7239445632000, 889141110912000, 129629670893568000, 22136856913815552000, 4377599743151480832000, 992559996665635184640000, 255805371399126806691840000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = gamma(2 + n)^2*(Pi^2/6 - 1 - digamma^(1)(2 + n)), where gamma(x) is the gamma function and digamma^(n)(x) is the n-th derivative of the digamma function. - Markus Bindhammer, Nov 26 2017
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EXAMPLE
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Let esf abbreviate "elementary symmetric function". Then
0th esf of {4}: 1;
1st esf of {4,9}: 4 + 9 = 13;
2nd esf of {4,9,16}: 4*9 + 4*16 + 9*16 = 244.
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MATHEMATICA
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f[k_] := (k + 1)^2; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 22}] (* A203156 *)
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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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