A238465 Generalized ordered Bell numbers Bo(8,n).

1, 8, 136, 3464, 117640, 4993928, 254396296, 15119104904, 1026912225160, 78468091562888, 6662087721342856, 622186077361470344, 63389713864392140680, 6996476832548305415048, 831619554631233264449416, 105909083171031626820475784

Offset: 0

Author

Vincenzo Librandi, Mar 18 2014

Keywords

• nonn

Comments

Row 8 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/(9 - 8*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]];

Mathematica

t = 30; Range[0, t]! CoefficientList[Series[1/(9 - 8 Exp[x]), {x, 0, t}], x]

Formula

E.g.f.: 1/(9 - 8*exp(x)).

a(n) ~ n! / (9*(log(9/8))^(n+1)). - Vaclav Kotesovec, Mar 20 2014

a(0) = 1; a(n) = 8*a(n-1) - 9*Sum_{k=1..n-1} (-1)^k * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Nov 17 2023