A172501 a(n) = binomial(n+8,8)*6^n.

1, 54, 1620, 35640, 641520, 10007712, 140107968, 1801388160, 21616657920, 244988789760, 2645878929408, 27420927086592, 274209270865920, 2657720625315840, 25058508752977920, 230538280527396864, 2074844524746571776, 18307451688940339200, 158664581304149606400

Offset: 0

Author

Zerinvary Lajos, Feb 05 2010

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n>=8) of 7 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (54,-1296,18144,-163296,979776,-3919104,10077696,-15116544,10077696).

Crossrefs

Cf. A081136, A081144, A139626, A036084, A050988, A141407.

Programs

Magma

[6^n* Binomial(n+8, 8): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Mathematica

Table[Binomial[n + 8, 8]*6^n, {n, 0, 20}]

PARI

Vec(1 / (1 - 6*x)^9 + O(x^30)) \\ Colin Barker, Jul 24 2017

Formula

From Colin Barker, Jul 24 2017: (Start)

G.f.: 1 / (1 - 6*x)^9.

a(n) = (2^(-7 + n)*3^(-2 + n)*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(6 + n)*(7 + n)*(8 + n)) / 35.

(End)

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 4785948/7 - 3750000*log(6/5).

Sum_{n>=0} (-1)^n/a(n) = 39530064*log(7/6) - 213275484/35. (End)