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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| S. Plouffe, Approximations de Series Generatrices et Quelques conjectures, Dissertation, Universite du Quebec a Montreal, 1992
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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FORMULA
| 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
| a[n_] := n(n + 1)(n + 2)(n^2 + 27n + 132)/5! Do[Print[n, " ", a[n]], {n, 1, 25}]
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PROG
| (PARI) a(n)=binomial(n+2, 3)*(n^2+27*n+132)/20 \\ Charles R Greathouse IV, Jul 29 2011
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CROSSREFS
| Cf. A000096, A006503, A006504.
Sequence in context: A128246 A204076 A163832 * A065762 A034009 A038732
Adjacent sequences: A139795 A139796 A139797 * A139799 A139800 A139801
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KEYWORD
| nonn,easy
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AUTHOR
| Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 22 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 23 2008
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