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A050982
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5-idempotent numbers.
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10
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1, 30, 525, 7000, 78750, 787500, 7218750, 61875000, 502734375, 3910156250, 29326171875, 213281250000, 1510742187500, 10458984375000, 70971679687500, 473144531250000, 3105010986328125, 20091247558593750
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,2
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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 (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 91, #43..
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LINKS
| Eric Weisstein's World of Mathematics, Idempotent Number
Index to sequences with linear recurrences with constant coefficients, signature (30,-375,2500,-9375,18750,-15625).
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FORMULA
| C(n, 5)*5^(n-5).
G.f.:1/(1-5*x)^6. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
Expansion of 1/(1-5*x)^6. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 02 2008
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MAPLE
| seq(binomial(n+5, 5)*5^n, n=0..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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PROG
| (Other) SAGE: [lucas_number2(n, 5, 0)*binomial(n, 5)/5^5 for n in xrange(5, 23)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 12 2009]
(PARI) a(n)=binomial(n, 5)*5^(n-5) \\ Charles R Greathouse IV, Sep 03 2011
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CROSSREFS
| Cf. A001788, A036216, A040075, A050988, A050989, A000389, A054849, A036219, A045543, A036084, A140404, A000389, A054849, A036219, A045543, A036084, A140404.
Sequence in context: A118681 A020926 A022754 * A004327 A139626 A037961
Adjacent sequences: A050979 A050980 A050981 * A050983 A050984 A050985
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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