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A139798
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Coefficient of x^5 in (1-x-x^2)^(-n).
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0
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8, 38, 111, 256, 511, 924, 1554, 2472, 3762, 5522, 7865, 10920, 14833, 19768, 25908, 33456, 42636, 53694, 66899, 82544, 100947, 122452, 147430, 176280, 209430, 247338, 290493, 339416, 394661, 456816, 526504, 604384, 691152, 787542
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OFFSET
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1,1
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COMMENTS
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The coefficient of x^5 in (1-x-x^2)^(-n) is the coefficient of x^5 in (1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5)^n. Using the multinomial theorem one then finds that a(n) = n(n+1)(n+2)(n^2 + 27n + 132)/5!
The inverse binomial transform yields 8,30,43,29,9,1,0,0,... (0 continued) - R. J. Mathar, May 23 2008
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REFERENCES
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Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
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LINKS
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FORMULA
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a(n) = n(n+1)(n+2)(n^2 + 27n + 132)/5!
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MATHEMATICA
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a[n_] := n(n + 1)(n + 2)(n^2 + 27n + 132)/5! Do[Print[n, " ", a[n]], {n, 1, 25}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {8, 38, 111, 256, 511, 924}, 40] (* Harvey P. Dale, Oct 13 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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