%I #23 Jan 12 2024 07:48:46
%S 1,7,105,2359,70665,2646007,118893705,6232661239,373405001865,
%T 25167452766967,1884759251911305,155262005162499319,
%U 13952854271421949065,1358385484966283220727,142418920493123648992905,15998363870912950298468599
%N Generalized ordered Bell numbers Bo(7,n).
%C Row 7 of array A094416, which has more information.
%H Vincenzo Librandi, <a href="/A238464/b238464.txt">Table of n, a(n) for n = 0..250</a>
%F E.g.f.: 1/(8 - 7*exp(x)).
%F a(n) ~ n! / (8*(log(8/7))^(n+1)). - _Vaclav Kotesovec_, Mar 20 2014
%F a(0) = 1; a(n) = 7*a(n-1) - 8*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/(8 - 7 Exp[x]), {x, 0, t}], x]
%o (Magma) m:=20; R<x>:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(8 - 7*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // _Bruno Berselli_, Mar 17 2014
%o (PARI) x='x+O('x^66); Vec(serlaplace(1/(8 - 7*exp(x)))) \\ _Joerg Arndt_, Mar 17 2014
%Y Cf. A000670, A004123, A032033, A094417, A094418, A094419.
%K nonn
%O 0,2
%A _Vincenzo Librandi_, Mar 17 2014
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