A173124 a(n) = binomial(n+10,10)*6^n.

1, 66, 2376, 61776, 1297296, 23351328, 373621248, 5444195328, 73496636928, 930957401088, 11171488813056, 127964326404096, 1407607590445056, 14942295960109056, 153692187018264576, 1536921870182645760, 14984988234280796160, 142798123173734645760, 1332782482954856693760

Offset

0,2

Comments

With a different offset, number of n-permutations (n>=10) of 7 objects: r, s, t, u, v, z, x, with repetition allowed, containing exactly 10 u's.

Links

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

Index entries for linear recurrences with constant coefficients, signature (66,-1980,35640,-427680,3592512,-21555072,92378880,-277136640,554273280,-665127936,362797056).

Formula

From Chai Wah Wu, Nov 12 2021: (Start)

a(n) = 66*a(n-1) - 1980*a(n-2) + 35640*a(n-3) - 427680*a(n-4) + 3592512*a(n-5) - 21555072*a(n-6) + 92378880*a(n-7) - 277136640*a(n-8) + 554273280*a(n-9) - 665127936*a(n-10) + 362797056*a(n-11) for n > 10.

G.f.: -1/(6*x - 1)^11. (End)

From Amiram Eldar, Sep 04 2022: (Start)

Sum_{n>=0} 1/a(n) = 897363955/42 - 117187500*log(6/5).

Sum_{n>=0} (-1)^n/a(n) = 2421216420*log(7/6) - 2239392937/6. (End)

Mathematica

Table[Binomial[n + 10, 10]*6^n, {n, 0, 20}]

Prog

(Magma) [6^n* Binomial(n+10, 10): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Crossrefs

Cf. A081136, A081144, A139626, A036084, A050988, A141407, A172501, A173123.

Sequence in context: A240464 A017729 A230993 * A004365 A062152 A138875

Adjacent sequences: A173121 A173122 A173123 * A173125 A173126 A173127

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 10 2010

Status

approved