A141407 a(n) = binomial(n+7,7)*6^n.

1, 48, 1296, 25920, 427680, 6158592, 80061696, 960740352, 10808328960, 115288842240, 1175946190848, 11545653510144, 109683708346368, 1012465000120320, 9112185001082880, 80187228009529344, 691614841582190592, 5858384540460908544, 48819871170507571200, 400836836978904268800

Offset

0,2

Comments

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

If n=7 then a(0)= 1 because we have uuuuuuu

a(1)=48 because we have

uuuuuuus, uuuuuuut, uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuuy,

uuuuuusu, uuuuuutu, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuuyu,

uuuuusuu, uuuuutuu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuuyuu,

uuuusuuu, uuuutuuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuuyuuu,

uuusuuuu, uuutuuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuuyuuuu,

uusuuuuu, uutuuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uuyuuuuu,

usuuuuuu, utuuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, uyuuuuuu,

suuuuuuu, tuuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu, yuuuuuuu.

Links

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

Index entries for linear recurrences with constant coefficients, signature (48,-1008,12096,-90720,435456,-1306368,2239488,-1679616).

Formula

O.g.f.: 1/(1-6x)^8. - R. J. Mathar, Aug 08 2008

a(n) = 48*a(n-1) - 1008*a(n-2) + 12096*a(n-3) - 90720*a(n-4) + 435456*a(n-5) - 1306368*a(n-6) + 2239488*a(n-7) - 1679616*a(n-8) for n > 7. - Chai Wah Wu, Nov 12 2021

From Amiram Eldar, Aug 29 2022: (Start)

Sum_{n>=0} 1/a(n) = 656250*log(6/5) - 239295/2.

Sum_{n>=0} (-1)^n/a(n) = 4941258*log(7/6) - 7616973/10. (End)

Maple

seq(binomial(n+7, 7)*6^n, n=0..16);

Mathematica

Table[Binomial[n + 7, 7] 6^n, {n, 0, 16}] (* Michael De Vlieger, Jul 24 2017 *)

Prog

(Magma) [6^n* Binomial(n+7, 7): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
(PARI) vector(15, n, binomial(n+6, 7)*6^(n-1)) \\ Derek Orr, Jul 24 2017

Crossrefs

Cf. A038255.

Sequence in context: A285169 A163272 A165283 * A004341 A222199 A288459

Adjacent sequences: A141404 A141405 A141406 * A141408 A141409 A141410

Keyword

nonn,easy

Author

Zerinvary Lajos, Aug 04 2008

Status

approved