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
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
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 12 2008
EXTENSIONS
More terms from Colin Barker, Sep 25 2013
STATUS
approved