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A024196
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a(n) = 2nd elementary symmetric function of the first n+1 odd positive integers.
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9
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3, 23, 86, 230, 505, 973, 1708, 2796, 4335, 6435, 9218, 12818, 17381, 23065, 30040, 38488, 48603, 60591, 74670, 91070, 110033, 131813, 156676, 184900, 216775, 252603, 292698, 337386, 387005, 441905, 502448, 569008, 641971, 721735, 808710, 903318
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = n*(n+1)*(3*n^2+5*n+1)/6.
G.f.: x*(3 + 8*x + x^2)/(1 - x)^5.
a(n) = Sum_{i=1..n} (n+1-i)*((n+1)^2-i).
a(n) = Sum_{i=1..n} ((2*i-1)*Sum_{j=i..n} (2*j+1)) = 1*(3+5+...2*n+1) + 3*(5+7+...+2*n+1) + ... + (2*n-1)*(2*n+1). - J. M. Bergot, Apr 21 2017
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EXAMPLE
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a(8) = 8*80+7*79+6*78+5*77+4*76+3*75+2*74+1*73 = 2796. - Bruno Berselli, Mar 13 2012
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MAPLE
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MATHEMATICA
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f[k_] := 2 k - 1; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 50}] (* A024196 *)
Table[(n(n+1)(3n^2+5n+1))/6, {n, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {3, 23, 86, 230, 505}, 50] (* Harvey P. Dale, Jul 08 2019 *)
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PROG
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(GAP) List([1..36], n -> n*(n+1)*(3*n^2+5*n+1)/6); # Muniru A Asiru, Feb 13 2018
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CROSSREFS
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Equals third right hand column of A028338 triangle.
Equals third left hand column of A109692 triangle.
Equals third right hand column of A161198 triangle divided by 2^m.
(End)
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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