OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations of 9 objects:
p, r, s, t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's. Example: a(1)=72 because we have
uuuuuuuup, uuuuuuupu, uuuuuupuu, uuuuupuuu, uuuupuuuu, uuupuuuuu, uupuuuuuu, upuuuuuuu, puuuuuuuu,
uuuuuuuur, uuuuuuuru, uuuuuuruu, uuuuuruuu, uuuuruuuu, uuuruuuuu, uuruuuuuu, uruuuuuuu, ruuuuuuuu,
uuuuuuuus, uuuuuuusu, uuuuuusuu, uuuuusuuu, uuuusuuuu, uuusuuuuu, uusuuuuuu, usuuuuuuu, suuuuuuuu,
uuuuuuuut, uuuuuuutu, uuuuuutuu, uuuuutuuu, uuuutuuuu, uuutuuuuu, uutuuuuuu, utuuuuuuu, tuuuuuuuu,
uuuuuuuuv, uuuuuuuvu, uuuuuuvuu, uuuuuvuuu, uuuuvuuuu, uuuvuuuuu, uuvuuuuuu, uvuuuuuuu, vuuuuuuuu,
uuuuuuuuz, uuuuuuuzu, uuuuuuzuu, uuuuuzuuu, uuuuzuuuu, uuuzuuuuu, uuzuuuuuu, uzuuuuuuu, zuuuuuuuu,
uuuuuuuux, uuuuuuuxu, uuuuuuxuu, uuuuuxuuu, uuuuxuuuu, uuuxuuuuu, uuxuuuuuu, uxuuuuuuu, xuuuuuuuu,
uuuuuuuuy, uuuuuuuyu, uuuuuuyuu, uuuuuyuuu, uuuuyuuuu, uuuyuuuuu, uuyuuuuuu, uyuuuuuuu, yuuuuuuuu.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
FORMULA
a(n) = binomial(n+8,8)*8^n.
G.f.: 1/(1-8*x)^9. - Vincenzo Librandi, Oct 16 2011
From Amiram Eldar, Apr 17 2022: (Start)
Sum_{n>=0} 1/a(n) = 738990736/105 - 52706752*log(8/7).
Sum_{n>=0} (-1)^n/a(n) = 306110016*log(9/8) - 1261909808/35. (End)
MAPLE
seq(binomial(n+8, 8)*8^n, n=0..17);
MATHEMATICA
Table[Binomial[n + 8, 8] 8^n, {n, 0, 15}] (* Michael De Vlieger, Jul 24 2017 *)
PROG
(Magma) [8^n* Binomial(n+8, 8): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
(PARI) vector(15, n, binomial(n+7, 8)*8^(n-1)) \\ Derek Orr, Jul 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Aug 01 2008
STATUS
approved