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A140107 a(n) = binomial(n+3, 3)*7^n.

%I A140107 #24 Aug 28 2022 04:21:22
%S A140107 1,28,490,6860,84035,941192,9882516,98825160,951192165,8877793540,
%T A140107 80787921214,719746934452,6297785676455,54257845827920,
%U A140107 461191689537320,3874010192113488,32202709721943369,265198785945415980,2165790085220897170,17554298585474640220
%N A140107 a(n) = binomial(n+3, 3)*7^n.
%C A140107 With a different offset, number of n-permutations (n=4) of 8 objects: s, t, u, v, w, z, x, y with repetition allowed, containing exactly three u's.
%C A140107 uuus, uusu, usuu, suuu,
%C A140107 uuut, uutu, utuu, tuuu,
%C A140107 uuuv, uuvu, uvuu, vuuu,
%C A140107 uuuw, uuwu, uwuu, wuuu,
%C A140107 uuuz, uuzu, uzuu, zuuu,
%C A140107 uuux, uuxu, uxuu, xuuu,
%C A140107 uuuy, uuyu, uyuu, yuuu
%H A140107 Vincenzo Librandi, <a href="/A140107/b140107.txt">Table of n, a(n) for n = 0..400</a>
%H A140107 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (28,-294,1372,-2401).
%F A140107 From _R. J. Mathar_, Jun 03 2009: (Start)
%F A140107 a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4).
%F A140107 G.f.: 1/(7*x-1)^4. (End)
%F A140107 From _Amiram Eldar_, Aug 28 2022: (Start)
%F A140107 Sum_{n>=0} 1/a(n) = 756*log(7/6) - 231/2.
%F A140107 Sum_{n>=0} (-1)^n/a(n) = 1344*log(8/7) - 357/2. (End)
%p A140107 seq(binomial(n+3,3)*7^n,n=0..26);
%t A140107 Table[Binomial[n+3,3]7^n,{n,0,20}] (* or *) LinearRecurrence[{28,-294,1372,-2401},{1,28,490,6860},20] (* _Harvey P. Dale_, Jun 21 2016 *)
%o A140107 (Magma) [7^n* Binomial(n+3, 3): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%o A140107 (PARI) a(n)=binomial(n+3,3)*7^n \\ _Charles R Greathouse IV_, Oct 07 2015
%K A140107 nonn,easy
%O A140107 0,2
%A A140107 _Zerinvary Lajos_, Jun 03 2008