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%I #20 Jan 12 2024 07:49:03
%S 1,9,171,4869,184851,8772309,499559571,33190014069,2520110222451,
%T 215270320769109,20431783142389971,2133148392099721269,
%U 242954208655633344051,29977118969127060357909,3983272698956314883956371,567091857051921058649396469
%N Generalized ordered Bell numbers Bo(9,n).
%C Row 9 of array A094416, which has more information.
%H Vincenzo Librandi, <a href="/A238466/b238466.txt">Table of n, a(n) for n = 0..250</a>
%F E.g.f.: 1/(10 - 9*exp(x)).
%F a(n) ~ n! / (10*(log(10/9))^(n+1)). - _Vaclav Kotesovec_, Mar 20 2014
%F a(0) = 1; a(n) = 9*a(n-1) - 10*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - _Seiichi Manyama_, Nov 17 2023
%t t=30; Range[0, t]! CoefficientList[Series[1/(10 - 9 Exp[x]), {x, 0, t}], x]
%o (Magma) m:=20; R<x>:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(10 - 9*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]];
%Y Cf. A000670, A004123, A032033, A094417, A094418, A094419, A238464.
%K nonn
%O 0,2
%A _Vincenzo Librandi_, Mar 18 2014
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