A140405 a(n) = binomial(n+6, 6)*5^n.

1, 35, 700, 10500, 131250, 1443750, 14437500, 134062500, 1173046875, 9775390625, 78203125000, 604296875000, 4532226562500, 33120117187500, 236572265625000, 1656005859375000, 11385040283203125, 77016448974609375, 513442993164062500, 3377914428710937500

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

Table of n, a(n) for n=0..19.

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

Cf. A000579, A002409, A036220, A036226, A050988, A054337, A140406.

Sequence in context: A202127 A175774 A112504 * A367250 A278361 A145603

Adjacent sequences: A140402 A140403 A140404 * A140406 A140407 A140408

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 16 2008

Status

approved