A238467 Generalized ordered Bell numbers Bo(10,n).

1, 10, 210, 6610, 277410, 14553010, 916146210, 67285818610, 5647734061410, 533307215001010, 55954905981282210, 6457903731351210610, 813080459351919805410, 110901542660769629769010, 16290196917457939734258210

Offset: 0

Author

Vincenzo Librandi, Mar 18 2014

Keywords

• nonn

Comments

Row 10 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/(11 - 10*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]];

Mathematica

t=30; Range[0, t]! CoefficientList[Series[1/(11 - 10 Exp[x]), {x, 0, t}], x]

Formula

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

a(n) ~ n! / (11*(log(11/10))^(n+1)). - Vaclav Kotesovec, Mar 20 2014

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