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A141407 a(n) = binomial(n+7,7)*6^n.

%I A141407 #29 Aug 29 2022 10:26:31
%S A141407 1,48,1296,25920,427680,6158592,80061696,960740352,10808328960,
%T A141407 115288842240,1175946190848,11545653510144,109683708346368,
%U A141407 1012465000120320,9112185001082880,80187228009529344,691614841582190592,5858384540460908544,48819871170507571200,400836836978904268800
%N A141407 a(n) = binomial(n+7,7)*6^n.
%C A141407 With a different offset, number of n-permutations (n>=7) of 7 objects: s, t, u, v, z, x, y with repetition allowed, containing exactly seven (7) u's.
%C A141407 If n=7 then a(0)= 1 because we have uuuuuuu
%C A141407 a(1)=48 because we have
%C A141407 uuuuuuus, uuuuuuut, uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuuy,
%C A141407 uuuuuusu, uuuuuutu, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuuyu,
%C A141407 uuuuusuu, uuuuutuu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuuyuu,
%C A141407 uuuusuuu, uuuutuuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuuyuuu,
%C A141407 uuusuuuu, uuutuuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuuyuuuu,
%C A141407 uusuuuuu, uutuuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uuyuuuuu,
%C A141407 usuuuuuu, utuuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, uyuuuuuu,
%C A141407 suuuuuuu, tuuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu, yuuuuuuu.
%H A141407 Vincenzo Librandi, <a href="/A141407/b141407.txt">Table of n, a(n) for n = 0..400</a>
%H A141407 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (48,-1008,12096,-90720,435456,-1306368,2239488,-1679616).
%F A141407 O.g.f.: 1/(1-6x)^8. - _R. J. Mathar_, Aug 08 2008
%F A141407 a(n) = 48*a(n-1) - 1008*a(n-2) + 12096*a(n-3) - 90720*a(n-4) + 435456*a(n-5) - 1306368*a(n-6) + 2239488*a(n-7) - 1679616*a(n-8) for n > 7. - _Chai Wah Wu_, Nov 12 2021
%F A141407 From _Amiram Eldar_, Aug 29 2022: (Start)
%F A141407 Sum_{n>=0} 1/a(n) = 656250*log(6/5) - 239295/2.
%F A141407 Sum_{n>=0} (-1)^n/a(n) = 4941258*log(7/6) - 7616973/10. (End)
%p A141407 seq(binomial(n+7,7)*6^n,n=0..16);
%t A141407 Table[Binomial[n + 7, 7] 6^n, {n, 0, 16}] (* _Michael De Vlieger_, Jul 24 2017 *)
%o A141407 (Magma) [6^n* Binomial(n+7, 7): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%o A141407 (PARI) vector(15,n,binomial(n+6,7)*6^(n-1)) \\ _Derek Orr_, Jul 24 2017
%Y A141407 Cf. A038255.
%K A141407 nonn,easy
%O A141407 0,2
%A A141407 _Zerinvary Lajos_, Aug 04 2008