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A173000
a(n) = binomial(n + 4, 4)*9^n.
8
1, 45, 1215, 25515, 459270, 7440174, 111602610, 1578379770, 21308126895, 277005649635, 3490271185401, 42835146366285, 514021756395420, 6049640671423020, 70002984912180660, 798034027998859524, 8977882814987169645, 99812932472504415465, 1097942257197548570115
OFFSET
0,2
COMMENTS
Number of n-permutations (n>=4) of 10 objects p, r, q, u, v, w, z, x, y, z with repetition allowed, containing exactly 4 u's.
LINKS
FORMULA
G.f.: 1/(1-9*x)^5. - R. J. Mathar, Dec 21 2011
a(n) = 45*a(n-1)-810*a(n-2)+7290*a(n-3)-32805*a(n-4)+59049*a(n-5). - Wesley Ivan Hurt, Apr 21 2021
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 2172 - 18432*log(9/8).
Sum_{n>=0} (-1)^n/a(n) = 36000*log(10/9) - 3792. (End)
a(n) = A000332(n+4)*A001019(n). - Michel Marcus, Aug 28 2022
MAPLE
A173000:=n->binomial(n+4, 4)*9^n: seq(A173000(n), n=0..25); # Wesley Ivan Hurt, Jul 24 2017
MATHEMATICA
Table[Binomial[n + 4, 4]*9^n, {n, 0, 20}]
PROG
(Magma) [Binomial(n+4, 4)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
(PARI) a(n)=binomial(n+4, 4)*9^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Sequence in context: A229796 A143400 A226981 * A004350 A199518 A075515
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 07 2010
STATUS
approved