A050989 7-idempotent numbers.
1, 56, 1764, 41160, 792330, 13311144, 201885684, 2826399576, 37096494435, 461645264080, 5493578642552, 62926446269232, 697434779483988, 7510836086750640, 78863778910881720, 809668130151718992, 8147285559651672357, 80514351413028291528, 782778416515552834300
Offset: 7
Links
- Vincenzo Librandi, Table of n, a(n) for n = 7..400
- Eric Weisstein's World of Mathematics, Idempotent Number.
- Index entries for linear recurrences with constant coefficients, signature (56,-1372,19208,-168070,941192,-3294172,6588344,-5764801).
Programs
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Magma
[7^(n-7)* Binomial(n, 7): n in [7..30]]; // Vincenzo Librandi, Oct 16 2011
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Maple
seq(binomial(n, 7)*7^(n-7), n=7..33); # Zerinvary Lajos, Aug 01 2008
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Mathematica
LinearRecurrence[{56,-1372,19208,-168070,941192,-3294172,6588344,-5764801}, {1,56,1764,41160,792330,13311144,201885684,2826399576},20] (* Harvey P. Dale, May 31 2014 *) -
PARI
a(n)=binomial(n, 7)*7^(n-7) \\ Charles R Greathouse IV, Sep 03 2011
Formula
a(n) = C(n, 7)*7^(n-7).
G.f.: x^7/(1-7*x)^8.
From Amiram Eldar, Apr 17 2022: (Start)
Sum_{n>=7} 1/a(n) = 2286144*log(7/6) - 10572289/30.
Sum_{n>=7} (-1)^(n+1)/a(n) = 12845056*log(8/7) - 51456517/30. (End)