A050988 6-idempotent numbers.

1, 42, 1008, 18144, 272160, 3592512, 43110144, 480370176, 5043886848, 50438868480, 484213137408, 4489976365056, 40409787285504, 354362750042112, 3037395000360960, 25514118003032064, 210491473525014528, 1708695490967764992, 13669563927742119936, 107917609955858841600

Offset: 6

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

Number of n-permutations of 7 objects: s, t, u, v, z, x, y with repetition allowed, containing exactly six u's. - Zerinvary Lajos, Jun 16 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 6..400
• Eric Weisstein's World of Mathematics, Idempotent Number.

Crossrefs

Cf. A000027, A001788, A036216, A040075, A050982, A050989.

Programs

Maple

seq(binomial(n, 6)*6^(n-6), n=6..32); # Zerinvary Lajos, Jun 16 2008
A050988:=x^6/(1-6*x)^7; series(A050988,x,32); # Zerinvary Lajos, Aug 09 2008

Mathematica

a[n_] := Binomial[n, 6]*6^(n - 6); Array[a, 20, 6] (* Amiram Eldar, Apr 17 2022 *)

Formula

a(n) = binomial(n,6)*6^(n-6).

G.f.: x^6/(1-6*x)^7. - Zerinvary Lajos, Aug 09 2008

From Amiram Eldar, Apr 17 2022: (Start)

Sum_{n>=6} 1/a(n) = 102561/5 - 112500*log(6/5).

Sum_{n>=6} (-1)^n/a(n) = 605052*log(7/6) - 466341/5. (End)