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 A268730 #24 Sep 08 2022 08:46:15
%S A268730 10,260,10920,633360,46868640,4218177600,447126825600,54549472723200,
%T A268730 7527827235801600,1159285394313446400,197078517033285888000,
%U A268730 36656604168191175168000,7404634041974617383936000,1614210221150466589698048000,377725191749209181989343232000
%N A268730 a(n) = Product_{k = 0..n} 2*(8*k + 5).
%H A268730 G. C. Greubel, <a href="/A268730/b268730.txt">Table of n, a(n) for n = 0..300</a>
%F A268730 a(n) = (2^(4*n + 13/4)*Gamma(1/8)*Gamma(n + 13/8))/(sqrt(Pi)*Gamma(1/4)), where Gamma(x) is the gamma function.
%F A268730 a(n) = 2*(8*n + 5)*a(n - 1), a(0)=10.
%F A268730 Sum_{n>=0} 1/a(n) = (exp(1/16)*(Gamma(5/8) - Gamma(5/8, 1/16)))/(2*sqrt(2)) = 0.10393932939417..., where Gamma(a, x) is the incomplete gamma function.
%F A268730 a(n) ~ sqrt(Pi) * 2^(4*n+9/2) * n^(n+9/8) / (Gamma(5/8) * exp(n)). - _Vaclav Kotesovec_, Feb 20 2016
%F A268730 G.f.: 10/(1-b(1)x/(1-(b(1)-10)x/(1-b(2)x/(1-(b(2)-10)x/(1-b(3)x/(...)))))), where b(n)=2(5+8n), i.e. 26,42,58,74. - _Benedict W. J. Irwin_, Feb 24 2016
%F A268730 a(n) = 2^(n+1)*A147625(n+2). - _R. J. Mathar_, Jun 07 2016
%F A268730 E.g.f.: 10/(1 - 16*x)^(13/8). - _Ilya Gutkovskiy_, Jun 07 2016
%e A268730 a(0) = (1 + 2 + 3 + 4) = 10;
%e A268730 a(1) = (1 + 2 + 3 + 4)*(5 + 6 + 7 + 8) = 260;
%e A268730 a(2) = (1 + 2 + 3 + 4)*(5 + 6 + 7 + 8) *(9 + 10 + 11 + 12) = 10920;
%e A268730 a(3) = (1 + 2 + 3 + 4)*(5 + 6 + 7 + 8) *(9 + 10 + 11 + 12)*(13 + 14 + 15 + 16) = 633360, etc.
%t A268730 FullSimplify[Table[(2^(4 n + 13/4) Gamma[1/8] Gamma[n + 13/8])/(Sqrt[Pi] Gamma[1/4]), {n, 0, 14}]]
%t A268730 Table[Product[16 k + 10, {k, 0, n - 1}], {n, 20}] (* _Vincenzo Librandi_, Feb 12 2016 *)
%o A268730 (Magma) [&*[(16*k+10): k in [0..n-1]]: n in [1..20]]; // _Vincenzo Librandi_, Feb 12 2016
%o A268730 (PARI) x='x+O('x^50); Vec(serlaplace(10/(1 - 16*x)^(13/8))) \\ _G. C. Greubel_, Apr 09 2017
%Y A268730 Cf. A000027, A113770, A147630.
%K A268730 nonn,easy
%O A268730 0,1
%A A268730 _Ilya Gutkovskiy_, Feb 12 2016