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A140405 a(n) = binomial(n+6, 6)*5^n. 2
1, 35, 700, 10500, 131250, 1443750, 14437500, 134062500, 1173046875, 9775390625, 78203125000, 604296875000, 4532226562500, 33120117187500, 236572265625000, 1656005859375000, 11385040283203125, 77016448974609375, 513442993164062500, 3377914428710937500 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=6) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's.
If n=6 then a(0)=1.
Example: a(1)=35 because we have
uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu,
uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu,
uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu,
uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu,
uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu.
LINKS
Index entries for linear recurrences with constant coefficients, signature (35,-525,4375,-21875,65625,-109375,78125).
FORMULA
G.f.: 1/(1-5*x)^7. - Zerinvary Lajos, Aug 06 2008
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 6856 - 30720*log(5/4).
Sum_{n>=0} (-1)^n/a(n) = 233280*log(6/5) - 42531. (End)
MAPLE
seq(binomial(n+6, 6)*5^n, n=0..18);
MATHEMATICA
Table[Binomial[n+6, 6]5^n, {n, 0, 20}] (* Harvey P. Dale, Dec 03 2017 *)
CROSSREFS
Sequence in context: A202127 A175774 A112504 * A367250 A278361 A145603
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 16 2008
STATUS
approved

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Last modified June 25 15:24 EDT 2024. Contains 373705 sequences. (Running on oeis4.)