A173191 a(n) = binomial(n + 6, 6)*9^n.

1, 63, 2268, 61236, 1377810, 27280638, 491051484, 8207574804, 129269303163, 1939039547445, 27922169483208, 388371993720984, 5243021915233284, 68965903654222428, 886704475554288360, 11172476391984033336, 138259395350802412533, 1683511461036241140843

Offset

0,2

Comments

Number of n-permutations (n>=6) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly six (6) u's.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (63,-1701,25515,-229635,1240029,-3720087,4782969).

Formula

a(n) = C(n + 6, 6)*9^n.

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 1042074/5 - 1769472*log(9/8).

Sum_{n>=0} (-1)^n/a(n) = 5400000*log(10/9) - 2844729/5. (End)

a(n) = 63*a(n-1) - 1701*a(n-2) + 25515*a(n-3) - 229635*a(n-4) + 1240029*a(n-5) - 3720087*a(n-6) + 4782969*a(n-7). - Wesley Ivan Hurt, Jun 05 2026

Maple

A173191:=n->binomial(n+6, 6)*9^n: seq(A173191(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017

Mathematica

Table[Binomial[n + 6, 6]*9^n, {n, 0, 20}]

Prog

(Magma) [Binomial(n+6, 6)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011

Crossrefs

Cf. A081139, A173000, A173187, A173188.

Sequence in context: A017726 A240421 A170932 * A143401 A075516 A004376

Adjacent sequences: A173188 A173189 A173190 * A173192 A173193 A173194

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 12 2010

Status

approved