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A024198
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4th elementary symmetric function of the first n+3 odd positive integers.
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5
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105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783, 17085783, 32645613, 59394517, 103613692, 174281212, 283927812, 449681892, 694529781, 1048818981, 1552033791, 2254874391, 3221672146, 4533175570, 6289743070
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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)*(n+2)*(n+3)*(15*n^4+150*n^3+515*n^2+672*n+223)/360.
G.f.: -x*(x^4+112*x^3+718*x^2+744*x+105) / (x-1)^9. - Colin Barker, Aug 15 2014
a(n) = A(n+4, n-1), n >= 1 (fifth diagonal). See a crossref. below. - Wolfdieter Lang, Jul 21 2017
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MATHEMATICA
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LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {105, 1689, 12139, 57379, 208054, 626934, 1646778, 3889578, 8439783}, 30] (* Harvey P. Dale, May 28 2018 *)
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PROG
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(PARI) Vec(-x*(x^4+112*x^3+718*x^2+744*x+105)/(x-1)^9 + O(x^100)) \\ Colin Barker, Aug 15 2014
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CROSSREFS
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Equals fifth right hand column of A028338 triangle.
Equals fifth left hand column of A109692 triangle.
Equals fifth 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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