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 A111598 #15 May 02 2022 02:59:22
%S A111598 1,72,3240,118800,3920400,122316480,3710266560,111307996800,
%T A111598 3339239904000,100919250432000,3088129063219200,96012739965542400,
%U A111598 3040403432242176000,98228418580131840000,3241537813144350720000
%N A111598 Lah numbers: a(n) = n!*binomial(n-1,7)/8!.
%D A111598 Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
%D A111598 John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
%H A111598 G. C. Greubel, <a href="/A111598/b111598.txt">Table of n, a(n) for n = 8..440</a>
%F A111598 E.g.f.: ((x/(1-x))^8)/8!.
%F A111598 a(n) = (n!/8!)*binomial(n-1, 8-1).
%F A111598 If we define f(n,i,x) = Sum_{k=i..n}(Sum_{j=i..k} (binomial(k,j)*Stirling1(n,k)* Stirling2(j,i)*x^(k-j) ) ) then a(n) = (-1)^n*f(n,8,-8), (n>=8). - _Milan Janjic_, Mar 01 2009
%F A111598 From _Amiram Eldar_, May 02 2022: (Start)
%F A111598 Sum_{n>=8} 1/a(n) = 61096*(gamma - Ei(1)) + 54544*e - 338732/5, where gamma = A001620, Ei(1) = A091725 and e = A001113.
%F A111598 Sum_{n>=8} (-1)^n/a(n) = 2107448*(gamma - Ei(-1)) - 1257760/e - 6080436/5, where Ei(-1) = -A099285. (End)
%t A111598 Table[(n-8)!*Binomial[n-1,7]*Binomial[n,8], {n,8,35}] (* _G. C. Greubel_, May 10 2021 *)
%o A111598 (Magma) [Factorial(n-8)*Binomial(n,8)*Binomial(n-1,7): n in [8..35]]; // _G. C. Greubel_, May 10 2021
%o A111598 (Sage) [factorial(n-8)*binomial(n,8)*binomial(n-1,7) for n in (8..35)] # _G. C. Greubel_, May 10 2021
%Y A111598 Column 8 of unsigned A008297 and A111596.
%Y A111598 Column 7 of A111597.
%Y A111598 Cf. A001113, A001620, A091725, A099285.
%K A111598 nonn,easy
%O A111598 8,2
%A A111598 _Wolfdieter Lang_, Aug 23 2005