A050989 7-idempotent numbers.

1, 56, 1764, 41160, 792330, 13311144, 201885684, 2826399576, 37096494435, 461645264080, 5493578642552, 62926446269232, 697434779483988, 7510836086750640, 78863778910881720, 809668130151718992, 8147285559651672357, 80514351413028291528, 782778416515552834300

Offset

7,2

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).

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)

Maple

seq(binomial(n, 7)*7^(n-7), n=7..33); # Zerinvary Lajos, Aug 01 2008

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 *)

Prog

(PARI) a(n)=binomial(n, 7)*7^(n-7) \\ Charles R Greathouse IV, Sep 03 2011
(Magma) [7^(n-7)* Binomial(n, 7): n in [7..30]]; // Vincenzo Librandi, Oct 16 2011

Crossrefs

Cf. A001788, A036216, A040075, A050982, A050988, A059297, A059300.

Sequence in context: A234761 A290607 A258465 * A333067 A140406 A075512

Adjacent sequences: A050986 A050987 A050988 * A050990 A050991 A050992

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved