OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=9) of 7 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly 9 u's.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (60,-1620,25920,-272160,1959552,-9797760,33592320,-75582720,100776960,-60466176).
FORMULA
a(n) = C(n + 9, 9)*6^n.
From Chai Wah Wu, Nov 12 2021: (Start)
a(n) = 60*a(n-1) - 1620*a(n-2) + 25920*a(n-3) - 272160*a(n-4) + 1959552*a(n-5) - 9797760*a(n-6) + 33592320*a(n-7) - 75582720*a(n-8) + 100776960*a(n-9) - 60466176*a(n-10) for n > 9.
G.f.: 1/(6*x - 1)^10. (End)
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 21093750*log(6/5) - 107683641/28.
Sum_{n>=0} (-1)^n/a(n) = 311299254*log(7/6) - 959739813/20. (End)
MATHEMATICA
Table[Binomial[n + 9, 9]*6^n, {n, 0, 20}]
PROG
(Magma) [6^n* Binomial(n+9, 9): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 10 2010
STATUS
approved