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A139626 a(n) = binomial(n+4, 4)*6^n.

%I A139626 #31 Aug 28 2022 04:20:04
%S A139626 1,30,540,7560,90720,979776,9797760,92378880,831409920,7205552640,
%T A139626 60526642176,495217981440,3961743851520,31084451758080,
%U A139626 239794342133760,1822437000216576,13668277501624320,101306056776744960,742911083029463040,5395880497792942080
%N A139626 a(n) = binomial(n+4, 4)*6^n.
%C A139626 With a different offset, number of n-permutations (n=5) of 7 objects t, u, v, w, z, x, y with repetition allowed, containing exactly four (4) u's. Example: a(1)=30 because we have
%C A139626 uuuut, uuutu, uutuu, utuuu, tuuuu,
%C A139626 uuuuv, uuuvu, uuvuu, uvuuu, vuuuu,
%C A139626 uuuuw, uuuwu, uuwuu, uwuuu, wuuuu,
%C A139626 uuuuz, uuuzu, uuzuu, uzuuu, zuuuu,
%C A139626 uuuux, uuuxu, uuxuu, uxuuu, xuuuu,
%C A139626 uuuuy, uuuyu, uuyuu, uyuuu, yuuuu.
%H A139626 Vincenzo Librandi, <a href="/A139626/b139626.txt">Table of n, a(n) for n = 0..400</a>
%H A139626 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (30,-360,2160,-6480,7776).
%F A139626 a(n) = A000332(n+4) * A000400(n). - _Michel Marcus_, Sep 11 2013
%F A139626 G.f.: 1 / (1-6*x)^5. - _Colin Barker_, Sep 25 2013
%F A139626 From _Amiram Eldar_, Aug 28 2022: (Start)
%F A139626 Sum_{n>=0} 1/a(n) = 548 - 3000*log(6/5).
%F A139626 Sum_{n>=0} (-1)^n/a(n) = 8232*log(7/6) - 1268. (End)
%p A139626 seq(binomial(n+4,4)*6^n,n=0..22);
%o A139626 (Magma) [6^n* Binomial(n+4, 4): n in [0..20]]; // _Vincenzo Librandi_, Oct 12 2011
%o A139626 (PARI) a(n)=binomial(n+4,4)*6^n \\ _Charles R Greathouse IV_, Sep 11 2013
%Y A139626 Cf. A000332, A000400.
%K A139626 nonn,easy
%O A139626 0,2
%A A139626 _Zerinvary Lajos_, Jun 12 2008
%E A139626 More terms from _Colin Barker_, Sep 25 2013