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%I #24 Jan 12 2024 07:48:58
%S 1,8,136,3464,117640,4993928,254396296,15119104904,1026912225160,
%T 78468091562888,6662087721342856,622186077361470344,
%U 63389713864392140680,6996476832548305415048,831619554631233264449416,105909083171031626820475784
%N Generalized ordered Bell numbers Bo(8,n).
%C Row 8 of array A094416, which has more information.
%H Vincenzo Librandi, <a href="/A238465/b238465.txt">Table of n, a(n) for n = 0..250</a>
%F E.g.f.: 1/(9 - 8*exp(x)).
%F a(n) ~ n! / (9*(log(9/8))^(n+1)). - _Vaclav Kotesovec_, Mar 20 2014
%F a(0) = 1; a(n) = 8*a(n-1) - 9*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/(9 - 8 Exp[x]), {x, 0, t}], x]
%o (Magma) m:=20; R<x>:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(9 - 8*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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