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 A177354 #24 Feb 27 2022 22:56:52
%S A177354 5,35,305,3095,35225,439775,5939225,85961375,1324702025,21632195375,
%T A177354 372965377625,6769644905375,129049505347625,2578419996023375,
%U A177354 53898389265685625,1176832196718869375,26798832693476455625,635575680349115699375,15677971277701873945625,401729457433222058609375
%N A177354 a(n) is the moment of order n for the density measure 24*x^4*exp(-x)/( (x^4*exp(-x)*Ei(x) - x^3 - x^2 - 2*x - 6)^2 + Pi^2*x^8*exp(-2*x) ) over the interval 0..infinity.
%C A177354 Ei(.) is the exponential integral.
%C A177354 This is the case k=4 in the family a(n,k) = (1/k!)*( (n+k+2)!-(k+1)*(n+k+1)! -Sum_{i=0..n-1} (n+k-i)!*a(i,k) ). The values k = 0 to 3 are represented by A003319, A111537, A111546, and A111556.
%C A177354 a(n,k) is the moment of order n for the density k!*x^k*exp(-x)/((x^k*exp(-x)*Ei(x) - Pk(x))^2 + Pi^2*x^(2*k)*exp(-2*x)) on the interval 0..infinity with polynomials Pk(x) = Sum_{i=0..k-1} (k-1-i)!*x^i.
%D A177354 R. Groux, Polynômes orthogonaux et transformations intégrales, Cépadués, 2008, 125-129.
%F A177354 a(n) = (1/24)*( (n+6)! - 5*(n+5)! - Sum_{i=0..n-1} (n+4-i)!*a(i) ).
%F A177354 a(n) = 5*A111532(n+1) (conjecture). - _R. J. Mathar_, Dec 14 2010
%F A177354 G.f.: 1/x/Q(0) - 1/x, where Q(k) = 1 - 3*x + k*x - x*(k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, May 04 2013
%F A177354 G.f.: (1-x-2/G(0))/x^2, where G(k) = 1 + 1/(1 - x*(k+1)/(x*(k-1) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 05 2013
%F A177354 G.f.: 1/x^2 - 5/x - 2/(x^2*G(0)), where G(k) = 1 + 1/(1 - x*(k+5)/(x*(k+5) + 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 06 2013
%o A177354 (PARI) a(n)=if(n==0, 5, (1/24)*( (n+6)! -5*(n+5)! -sum(i=0,n-1, (n+4-i)!*a(i) ) ) ); \\ _Joerg Arndt_, May 04 2013
%K A177354 nonn
%O A177354 0,1
%A A177354 _Groux Roland_, Dec 10 2010