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

0,2

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).

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)

Maple

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

Prog

(Magma) [6^n* Binomial(n+4, 4): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
(PARI) a(n)=binomial(n+4, 4)*6^n \\ Charles R Greathouse IV, Sep 11 2013

Crossrefs

Cf. A000332, A000400.

Sequence in context: A004327 A270499 A286975 * A037961 A143399 A293103

Adjacent sequences: A139623 A139624 A139625 * A139627 A139628 A139629

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 12 2008

Extensions

More terms from Colin Barker, Sep 25 2013

Status

approved