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URL: https://oeis.org/A139798

⇱ A139798 - OEIS

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A139798
Coefficient of x^5 in (1-x-x^2)^(-n).
0
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
OFFSET
1,1
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, May 23 2008
REFERENCES
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
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, May 23 2008
MATHEMATICA
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 *)
PROG
(PARI) a(n)=binomial(n+2, 3)*(n^2+27*n+132)/20 \\ Charles R Greathouse IV, Jul 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sergio Falcon, May 22 2008
EXTENSIONS
More terms from R. J. Mathar, May 23 2008
STATUS
approved