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

%I A139641 #18 Aug 28 2022 04:20:55
%S A139641 1,35,735,12005,168070,2117682,24706290,271769190,2853576495,
%T A139641 28852829005,282757724249,2699051004195,25191142705820,
%U A139641 230595844768660,2075362602917940,18401548412539068,161013548609716845,1392293626213433895,11911845468714934435,100937216866479181265
%N A139641 a(n) = binomial(n+4, 4)*7^n.
%C A139641 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
%C A139641 uuuus, uuusu, uusuu, usuuu, suuuu,
%C A139641 uuuut, uuutu, uutuu, utuuu, tuuuu,
%C A139641 uuuuv, uuuvu, uuvuu, uvuuu, vuuuu,
%C A139641 uuuuw, uuuwu, uuwuu, uwuuu, wuuuu,
%C A139641 uuuuz, uuuzu, uuzuu, uzuuu, zuuuu,
%C A139641 uuuux, uuuxu, uuxuu, uxuuu, xuuuu,
%C A139641 uuuuy, uuuyu, uuyuu, uyuuu, yuuuu.
%H A139641 Vincenzo Librandi, <a href="/A139641/b139641.txt">Table of n, a(n) for n = 0..400</a>
%H A139641 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (35,-490,3430,-12005,16807).
%F A139641 From _Amiram Eldar_, Aug 28 2022: (Start)
%F A139641 Sum_{n>=0} 1/a(n) = 2800/3 - 6048*log(7/6).
%F A139641 Sum_{n>=0} (-1)^n/a(n) = 14336*log(8/7) - 5740/3. (End)
%p A139641 seq(binomial(n+4,4)*7^n,n=0..20);
%t A139641 Table[7^n * Binomial[n+4, 4], {n, 0, 20}] (* _Amiram Eldar_, Aug 28 2022 *)
%o A139641 (Magma) [7^n* Binomial(n+4, 4): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%K A139641 nonn,easy
%O A139641 0,2
%A A139641 _Zerinvary Lajos_, Jun 12 2008