A238467 - OEIS

%I #20 Jan 12 2024 07:49:07

%S 1,10,210,6610,277410,14553010,916146210,67285818610,5647734061410,

%T 533307215001010,55954905981282210,6457903731351210610,

%U 813080459351919805410,110901542660769629769010,16290196917457939734258210

%N Generalized ordered Bell numbers Bo(10,n).

%C Row 10 of array A094416, which has more information.

%H Vincenzo Librandi, <a href="/A238467/b238467.txt">Table of n, a(n) for n = 0..250</a>

%F E.g.f.: 1/(11 - 10*exp(x)).

%F a(n) ~ n! / (11*(log(11/10))^(n+1)). - _Vaclav Kotesovec_, Mar 20 2014

%F a(0) = 1; a(n) = 10*a(n-1) - 11*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/(11 - 10 Exp[x]), {x, 0, t}], x]

%o (Magma) m:=20; R<x>:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(11 - 10*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