A139641 a(n) = binomial(n+4, 4)*7^n.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (35,-490,3430,-12005,16807).

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

Adjacent sequences: A139638 A139639 A139640 * A139642 A139643 A139644

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 12 2008

Status

approved