A238466 Generalized ordered Bell numbers Bo(9,n).

1, 9, 171, 4869, 184851, 8772309, 499559571, 33190014069, 2520110222451, 215270320769109, 20431783142389971, 2133148392099721269, 242954208655633344051, 29977118969127060357909, 3983272698956314883956371, 567091857051921058649396469

Offset: 0

Author

Vincenzo Librandi, Mar 18 2014

Keywords

• nonn

Comments

Row 9 of array A094416, which has more information.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000670, A004123, A032033, A094417, A094418, A094419, A238464.

Programs

Magma

m:=20; R:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(10 - 9*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]];

Mathematica

t=30; Range[0, t]! CoefficientList[Series[1/(10 - 9 Exp[x]), {x, 0, t}], x]

Formula

E.g.f.: 1/(10 - 9*exp(x)).

a(n) ~ n! / (10*(log(10/9))^(n+1)). - Vaclav Kotesovec, Mar 20 2014

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