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
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 10 2010
STATUS
approved