This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A054338 #30 Jun 08 2025 19:43:53
%S A054338 1,32,576,7680,84480,811008,7028736,56229888,421724160,2998927360,
%T A054338 20392706048,133479530496,845370359808,5202279137280,31213674823680,
%U A054338 183120225632256,1052941297385472,5946021444059136,33033452466995200,180814687187763200,976399310813921280
%N A054338 8-fold convolution of A000302 (powers of 4).
%C A054338 With a different offset, number of n-permutations (n>=7) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly seven (7) u's. - _Zerinvary Lajos_, Jun 23 2008
%H A054338 Vincenzo Librandi, <a href="/A054338/b054338.txt">Table of n, a(n) for n = 0..400</a>
%H A054338 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (32,-448,3584,-17920,57344,-114688,131072,-65536).
%F A054338 a(n) = binomial(n+7, 7)*4^n.
%F A054338 G.f.: 1/(1-4*x)^8.
%F A054338 a(n) = A054335(n+15, 15).
%F A054338 E.g.f.: (315 + 8820*x + 52920*x^2 + 117600*x^3 + 117600*x^4 + 56448*x^5 + 12544*x^6 + 1024*x^7)*exp(4*x)/315. - _G. C. Greubel_, Jul 21 2019
%F A054338 From _Amiram Eldar_, Mar 27 2022: (Start)
%F A054338 Sum_{n>=0} 1/a(n) = 20412*log(4/3) - 88067/15.
%F A054338 Sum_{n>=0} (-1)^n/a(n) = 437500*log(5/4) - 292873/3. (End)
%p A054338 seq(binomial(n+7,7)*4^n,n=0..20); # _Zerinvary Lajos_, Jun 23 2008
%t A054338 Table[4^n*Binomial[n+7,7], {n,0,20}] (* _G. C. Greubel_, Jul 21 2019 *)
%t A054338 LinearRecurrence[{32,-448,3584,-17920,57344,-114688,131072,-65536},{1,32,576,7680,84480,811008,7028736,56229888},30] (* _Harvey P. Dale_, Jun 08 2025 *)
%o A054338 (Magma) [4^n*Binomial(n+7, 7): n in [0..20]]; // _Vincenzo Librandi_, Oct 15 2011
%o A054338 (PARI) vector(20, n, n--; 4^n*binomial(n+7,7)) \\ _G. C. Greubel_, Jul 21 2019
%o A054338 (GAP) List([0..20], n-> 4^n*Binomial(n+7,7) ); # _G. C. Greubel_, Jul 21 2019
%Y A054338 Cf. A000302, A054335.
%Y A054338 Cf. A038231.
%K A054338 easy,nonn
%O A054338 0,2
%A A054338 _Wolfdieter Lang_, Mar 13 2000