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 A047056 #44 Dec 19 2022 01:56:07
%S A047056 1,3,24,312,5616,129168,3616704,119351232,4535346816,195019913088,
%T A047056 9360955828224,496130658895872,28775578215960576,1812861427605516288,
%U A047056 123274577077175107584,8999044126633782853632,701925441877435062583296,58259811675827110194413568
%N A047056 Quintuple factorial numbers: Product_{k=0..n-1} (5*k+3).
%H A047056 G. C. Greubel, <a href="/A047056/b047056.txt">Table of n, a(n) for n = 0..350</a>
%F A047056 E.g.f.: (1-5*x)^(-3/5).
%F A047056 a(n) ~ sqrt(2*Pi)/Gamma(3/5)*n^(1/10)*(5*n/e)^n*(1 - 11/300*n^ - 1 + ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001
%F A047056 G.f.: 1/(1-3*x/(1-5*x/(1-8*x/(1-10*x/(1-13*x/(1-15*x/(1-18*x/(1-20*x/(1- ... (continued fraction). - _Philippe Deléham_, Jan 08 2012
%F A047056 a(n) = (-2)^n*Sum_{k=0..n} (5/2)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - _Mircea Merca_, May 03 2012
%F A047056 G.f.: 1/G(0) where G(k) = 1 - x*(5*k+3)/( 1 - 5*x*(k+1)/G(k+1) ); (continued fraction ). - _Sergei N. Gladkovskii_, Mar 23 2013
%F A047056 G.f.: G(0)/2, where G(k)= 1 + 1/(1 - (5*k+3)*x/((5*k+3)*x + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 14 2013
%F A047056 D-finite with recurrence: a(n) +(-5*n+2)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020
%F A047056 Sum_{n>=0} 1/a(n) = 1 + (e/5^2)^(1/5)*(Gamma(3/5) - Gamma(3/5, 1/5)). - _Amiram Eldar_, Dec 19 2022
%p A047056 seq(mul(5*k+3, k = 0..n-1), n = 0..20); # _G. C. Greubel_, Aug 20 2019
%t A047056 Table[5^n*Pochhammer[3/5, n], {n,0,20}] (* _G. C. Greubel_, Aug 20 2019 *)
%t A047056 Join[{1},FoldList[Times,5*Range[0,20]+3]] (* _Harvey P. Dale_, Oct 08 2020 *)
%o A047056 (PARI) vector(20, n, n--; prod(j=0,n-1, 5*j+3) ) \\ _G. C. Greubel_, Aug 20 2019
%o A047056 (Magma) [1] cat [(&*[5*k+3: k in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Aug 20 2019
%o A047056 (Sage) [5^n*rising_factorial(3/5, n) for n in (0..20)] # _G. C. Greubel_, Aug 20 2019
%o A047056 (GAP) List([0..20], n-> Product([0..n-1], k-> 5*k+3 )); # _G. C. Greubel_, Aug 20 2019
%Y A047056 Cf. A008546, A008548, A047055, A048994, A052562.
%K A047056 nonn,easy
%O A047056 0,2
%A A047056 Joe Keane (jgk(AT)jgk.org)