A139626 a(n) = binomial(n+4, 4)*6^n.

1, 30, 540, 7560, 90720, 979776, 9797760, 92378880, 831409920, 7205552640, 60526642176, 495217981440, 3961743851520, 31084451758080, 239794342133760, 1822437000216576, 13668277501624320, 101306056776744960, 742911083029463040, 5395880497792942080

Offset: 0

Author

Zerinvary Lajos, Jun 12 2008

Keywords

• nonn
• easy

Comments

With a different offset, number of n-permutations (n=5) of 7 objects t, u, v, w, z, x, y with repetition allowed, containing exactly four (4) u's. Example: a(1)=30 because we have

uuuut, uuutu, uutuu, utuuu, tuuuu,

uuuuv, uuuvu, uuvuu, uvuuu, vuuuu,

uuuuw, uuuwu, uuwuu, uwuuu, wuuuu,

uuuuz, uuuzu, uuzuu, uzuuu, zuuuu,

uuuux, uuuxu, uuxuu, uxuuu, xuuuu,

uuuuy, uuuyu, uuyuu, uyuuu, yuuuu.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..400
• Index entries for linear recurrences with constant coefficients, signature (30,-360,2160,-6480,7776).

Crossrefs

Cf. A000332, A000400.

Programs

Magma

[6^n* Binomial(n+4, 4): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011

Maple

seq(binomial(n+4,4)*6^n,n=0..22);

PARI

a(n)=binomial(n+4,4)*6^n \\ Charles R Greathouse IV, Sep 11 2013

Formula

a(n) = A000332(n+4) * A000400(n). - Michel Marcus, Sep 11 2013

G.f.: 1 / (1-6*x)^5. - Colin Barker, Sep 25 2013

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 548 - 3000*log(6/5).

Sum_{n>=0} (-1)^n/a(n) = 8232*log(7/6) - 1268. (End)

Extensions

More terms from Colin Barker, Sep 25 2013