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Search: id:A139798
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| A139798 |
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Coefficient of x^5 in (1-x-x^2)^(-n). |
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+0
1
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (mathar(AT)strw.leidenuniv.nl), May 23 2008
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REFERENCES
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S. Plouffe, Approximations de Series Generatrices et Quelques conjectures, Dissertation, Universite du Quebec a Montreal, 1992
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FORMULA
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a(n) = n(n+1)(n+2)(n^2+27n+132)/5!
O.g.f.: x(3x-4)(x-2)/(1-x)^6. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 23 2008
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MATHEMATICA
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Clear["Global`*"] a[n_] := n(n + 1)(n + 2)(n^2 + 27n + 132)/5! Do[Print[n, " ", a[n]], {n, 1, 25}]
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CROSSREFS
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Cf. A000027, A000096, A006503, A006504.
Sequence in context: A111645 A128246 A163832 this_sequence A065762 A034009 A038732
Adjacent sequences: A139795 A139796 A139797 this_sequence A139799 A139800 A139801
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KEYWORD
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nonn
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AUTHOR
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Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 22 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 23 2008
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