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 A111599 #24 Jan 20 2025 20:23:51
%S A111599 1,90,4950,217800,8494200,309188880,10821610800,371026656000,
%T A111599 12614906304000,428906814336000,14668613050291200,506733905373696000,
%U A111599 17735686688079360000,630299019222512640000,22780807409042242560000
%N A111599 Lah numbers: a(n) = n!*binomial(n-1,8)/9!.
%D A111599 Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
%D A111599 John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
%F A111599 E.g.f.: ((x/(1-x))^9)/9!.
%F A111599 a(n) = (n!/9!)*binomial(n-1, 9-1).
%F A111599 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-1)*f(n,9,-9), n >= 9. - _Milan Janjic_, Mar 01 2009
%F A111599 From _Amiram Eldar_, May 02 2022: (Start)
%F A111599 Sum_{n>=9} 1/a(n) = 564552*(Ei(1) - gamma) - 264528*e - 873657/35, where Ei(1) = A091725, gamma = A001620, and e = A001113.
%F A111599 Sum_{n>=9} (-1)^(n+1)/a(n) = 28393416*(gamma - Ei(-1)) - 16938720/e - 573537159/35, where Ei(-1) = -A099285. (End)
%p A111599 part_ZL:=[S,{S=Set(U,card=r),U=Sequence(Z,card>=1)}, labeled]: seq(count(subs(r=9,part_ZL),size=m),m=9..23) ; # _Zerinvary Lajos_, Mar 09 2007
%t A111599 Table[n!*Binomial[n-1, 8]/9!, {n, 9, 30}] (* _Wesley Ivan Hurt_, Dec 10 2013 *)
%Y A111599 Column 9 of unsigned A008297 and A111596.
%Y A111599 Column 8: A111598.
%Y A111599 Cf. A001113, A001620, A091725, A099285.
%K A111599 nonn,easy
%O A111599 9,2
%A A111599 _Wolfdieter Lang_, Aug 23 2005