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A139641
a(n) = binomial(n+4, 4)*7^n.
6
1, 35, 735, 12005, 168070, 2117682, 24706290, 271769190, 2853576495, 28852829005, 282757724249, 2699051004195, 25191142705820, 230595844768660, 2075362602917940, 18401548412539068, 161013548609716845, 1392293626213433895, 11911845468714934435, 100937216866479181265
OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n=5) of 8 objects s, t, u, v, w, z, x, y with repetition allowed, containing exactly four (4) u's. Example: a(1)=35 because we have
uuuus, uuusu, uusuu, usuuu, suuuu,
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
FORMULA
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 2800/3 - 6048*log(7/6).
Sum_{n>=0} (-1)^n/a(n) = 14336*log(8/7) - 5740/3. (End)
MAPLE
seq(binomial(n+4, 4)*7^n, n=0..20);
MATHEMATICA
Table[7^n * Binomial[n+4, 4], {n, 0, 20}] (* Amiram Eldar, Aug 28 2022 *)
PROG
(Magma) [7^n* Binomial(n+4, 4): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
CROSSREFS
Sequence in context: A278361 A145603 A326865 * A240928 A028220 A334909
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 12 2008
STATUS
approved