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 A001707 M4947 N2119 #29 Jan 01 2023 12:36:03
%S A001707 1,14,155,1665,18424,214676,2655764,34967140,489896616,7292774280,
%T A001707 115119818736,1922666722704,33896996544384,629429693586048,
%U A001707 12283618766690304,251426391808144896,5387217520095244800,120615281647055884800,2817014230489985049600
%N A001707 Generalized Stirling numbers.
%C A001707 The asymptotic expansion of the higher order exponential integral E(x,m=4,n=2) ~ exp(-x)/x^4*(1 - 14/x + 155/x^2 - 1665/x^3 + 18424/x^4 - 214676/x^5 + ...) leads to the sequence given above. See A163931 and A163934 for more information. - _Johannes W. Meijer_, Oct 20 2009
%D A001707 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001707 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001707 T. D. Noe, <a href="/A001707/b001707.txt">Table of n, a(n) for n = 0..100</a>
%H A001707 D. S. Mitrinovic and M. S. Mitrinovic, <a href="http://pefmath2.etf.rs/files/47/77.pdf">Tableaux d'une classe de nombres reliés aux nombres de Stirling</a>, Univ. Beograd. Pubi. Elektrotehn. Fak. Ser. Mat. Fiz. 77 (1962).
%H A001707 Robert E. Moritz, <a href="/A001701/a001701.pdf">On the sum of products of n consecutive integers</a>, Univ. Washington Publications in Math., 1 (No. 3, 1926), 44-49 [Annotated scanned copy]
%F A001707 E.g.f.: - log ( 1 - x )^3 / 6 ( x - 1 )^2.
%F A001707 a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(k+3, 3)*2^k*Stirling1(n+3, k+3). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
%F A001707 If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-3) = |f(n,3,2)|, for n>=3. [From _Milan Janjic_, Dec 21 2008]
%t A001707 nn = 23; t = Range[0, nn]! CoefficientList[Series[-Log[1 - x]^3/(6*(1 - x)^2), {x, 0, nn}], x]; Drop[t, 3] (* _T. D. Noe_, Aug 09 2012 *)
%o A001707 (PARI) a(n) = sum(k=0, n, (-1)^(n+k)*binomial(k+3, 3)*2^k*stirling(n+3, k+3, 1)); \\ _Michel Marcus_, Jan 01 2023
%K A001707 nonn
%O A001707 0,2
%A A001707 _N. J. A. Sloane_
%E A001707 More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004