A173113 a(n) = binomial(n + 10, 10) * 5^n.

1, 55, 1650, 35750, 625625, 9384375, 125125000, 1519375000, 17092968750, 180425781250, 1804257812500, 17222460937500, 157872558593750, 1396564941406250, 11970556640625000, 99754638671875000

Offset

0,2

Comments

With a different offset, number of n-permutations (n>=10) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly ten (10) u's.

Links

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

Index entries for linear recurrences with constant coefficients, signature (55,-1375,20625,-206250,1443750,-7218750,25781250,-64453125,107421875,-107421875,48828125).

Formula

a(n) = C(n + 10, 10)*5^n, n>=0.

G.f.: 1/(1-5*x)^11. - Vincenzo Librandi, Oct 15 2011

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 184261655/63 - 13107200*log(5/4).

Sum_{n>=0} (-1)^n/a(n) = 503884800*log(6/5) - 11575501585/126. (End)

Mathematica

Table[Binomial[n + 10, 10]*5^n, {n, 0, 20}]

Prog

(Magma) [5^n*Binomial(n+10, 10): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011

Crossrefs

Cf. A053464, A084902, A081143, A036071, A050982, A140405, A140220, A140346, A140520.

Sequence in context: A271796 A222836 A017718 * A166844 A077688 A188712

Adjacent sequences: A173110 A173111 A173112 * A173114 A173115 A173116

Keyword

nonn,easy

Author

Zerinvary Lajos, Feb 10 2010

Status

approved