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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

With a different offset, number of n-permutations of 6 objects:t,u,v,z,x, y with repetition allowed, containing exactly five (5) u's. Example: a(1)=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

L. 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

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

(Sage) [lucas_number2(n, 5, 0)*binomial(n, 5)/5^5 for n in xrange(5, 23)] # Zerinvary Lajos, Mar 12 2009

(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 November 20 08:16 EST 2018. Contains 317385 sequences. (Running on oeis4.)