A238464 Generalized ordered Bell numbers Bo(7,n).

1, 7, 105, 2359, 70665, 2646007, 118893705, 6232661239, 373405001865, 25167452766967, 1884759251911305, 155262005162499319, 13952854271421949065, 1358385484966283220727, 142418920493123648992905, 15998363870912950298468599

Offset: 0

Author

Vincenzo Librandi, Mar 17 2014

Keywords

• nonn

Comments

Row 7 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.

Programs

Magma

m:=20; R:=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

Mathematica

t=30; Range[0, t]! CoefficientList[Series[1/(8 - 7 Exp[x]), {x, 0, t}], x]

PARI

x='x+O('x^66); Vec(serlaplace(1/(8 - 7*exp(x)))) \\ Joerg Arndt, Mar 17 2014

Formula

E.g.f.: 1/(8 - 7*exp(x)).

a(n) ~ n! / (8*(log(8/7))^(n+1)). - Vaclav Kotesovec, Mar 20 2014

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