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%I #14 May 02 2022 02:59:30
%S 1,110,7260,377520,17177160,721440720,28857628800,1121325004800,
%T 42890681433600,1629845894476800,61934143990118400,
%U 2364758225077248000,91043191665474048000,3543681152517682176000,139722285442125754368000
%N Lah numbers: a(n) = n!*binomial(n-1,9)/10!.
%D Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
%D John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
%F E.g.f.: ((x/(1-x))^10)/10!.
%F a(n) = (n!/10!)*binomial(n-1, 10-1).
%F If we define f(n,i,x) = Sum_{k=1..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i)*x^(k-j) then a(n) = (-1)^n*f(n,10,-10), (n>=10). - _Milan Janjic_, Mar 01 2009
%F From _Amiram Eldar_, May 02 2022: (Start)
%F Sum_{n>=10} 1/a(n) = 5086710*(gamma - Ei(1)) + 50940*e + 91914449/14, where gamma = A001620, Ei(1) = A091725 and e = A001113.
%F Sum_{n>=10} (-1)^n/a(n) = 413689770*(gamma - Ei(-1)) - 246749400/e - 3342795017/14, where Ei(-1) = -A099285. (End)
%t Table[n! * Binomial[n - 1, 9]/10!, {n, 10, 25}] (* _Amiram Eldar_, May 02 2022 *)
%Y Column 10 of unsigned A008297 and A111596.
%Y Column 9: A111599.
%Y Cf. A001113, A001620, A091725, A099285.
%K nonn,easy
%O 10,2
%A _Wolfdieter Lang_, Aug 23 2005