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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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6
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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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COMMENTS
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This sequence is related to A016061 by the transform a(n) = n*A016061(n)-sum(A016061(i), i=0..n-1). - Bruno Berselli, Mar 13 2012
Partials sums of A099721. - Philippe Deléham, May 07 2012
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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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. - Bruno Berselli, Mar 13 2012
a(n) = sum((n+1-i)*((n+1)^2-i), i=1..n). - Bruno Berselli, Mar 13 2012
a(n) - a(n-1) = A099721(n). - Philippe Deléham, May 07 2012
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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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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 *)
(* Clark Kimberling, Dec 31 2011 *)
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CROSSREFS
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Contribution from Johannes W. Meijer, Jun 08 2009: (Start)
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)
Cf. A016061.
Sequence in context: A201482 A032017 A197453 * A196339 A196318 A213846
Adjacent sequences: A024193 A024194 A024195 * A024197 A024198 A024199
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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