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 A050982 5-idempotent numbers. 11
 1, 30, 525, 7000, 78750, 787500, 7218750, 61875000, 502734375, 3910156250, 29326171875, 213281250000, 1510742187500, 10458984375000, 70971679687500, 473144531250000, 3105010986328125, 20091247558593750, 128360748291015625, 810699462890625000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,2 COMMENTS Number of n-permutations of 6 objects: t,u,v,z,x, y with repetition allowed, containing exactly five u's. Example: a(6)=30 because we have uuuuut, uuuutu, uuutuu, uutuuu, utuuuu, tuuuuu, uuuuuv, uuuuvu, uuuvuu, uuvuuu, uvuuuu, vuuuuu, uuuuuz, uuuuzu, uuuzuu, uuzuuu, uzuuuu, zuuuuu, uuuuux, uuuuxu, uuuxuu, uuxuuu, uxuuuu, xuuuuu, uuuuuy, uuuuyu, uuuyuu, uuyuuu, uyuuuu, yuuuuu. - Zerinvary Lajos, Jun 16 2008 REFERENCES Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #43. LINKS Vincenzo Librandi, Table of n, a(n) for n = 5..1000 Eric Weisstein's World of Mathematics, Idempotent Number. Index entries for linear recurrences with constant coefficients, signature (30,-375,2500,-9375,18750,-15625). FORMULA a(n) = C(n, 5)*5^(n-5). G.f.: x^5/(1-5*x)^6. - Zerinvary Lajos, Aug 06 2008 From Amiram Eldar, Apr 17 2022: (Start) Sum_{n>=5} 1/a(n) = 6400*log(5/4) - 17125/12. Sum_{n>=5} (-1)^(n+1)/a(n) = 32400*log(6/5) - 23625/4. (End) MAPLE seq(binomial(n, 5)*5^(n-5), n=5..32); # Zerinvary Lajos, Jun 16 2008 MATHEMATICA CoefficientList[Series[1 / (1 - 5 x)^6, {x, 0, 33}], x] (* Vincenzo Librandi, Aug 12 2017 *) PROG (PARI) a(n)=binomial(n, 5)*5^(n-5) \\ Charles R Greathouse IV, Sep 03 2011 (Magma) [Binomial(n, 5)*5^(n-5): n in [5..25]]; // Vincenzo Librandi, Aug 12 2017 CROSSREFS Cf. A001788, A036216, A040075, A050988, A050989, A000389, A054849, A036219, A045543, A036084, A140404, A000389, A054849, A036219, A045543, A036084, A140404. Sequence in context: A020926 A229563 A022754 * A004327 A270499 A286975 Adjacent sequences: A050979 A050980 A050981 * A050983 A050984 A050985 KEYWORD nonn,easy AUTHOR Eric W. Weisstein STATUS approved

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Last modified August 7 06:13 EDT 2024. Contains 375008 sequences. (Running on oeis4.)