A173123 a(n) = binomial(n+9,9)*6^n.

1, 60, 1980, 47520, 926640, 15567552, 233513280, 3202467840, 40831464960, 489977579520, 5585744406528, 60935393525760, 639821632020480, 6496650417438720, 64038411257610240, 614768748073058304, 5763457013184921600, 52888193768049868800, 475993743912448819200

Offset: 0

Author

Zerinvary Lajos, Feb 10 2010

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

[6^n* Binomial(n+9, 9): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Mathematica

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

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)