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A094417 Generalized ordered Bell numbers Bo(4,n). 11
1, 4, 36, 484, 8676, 194404, 5227236, 163978084, 5878837476, 237109864804, 10625889182436, 523809809059684, 28168941794178276, 1641079211868751204, 102961115527874385636, 6921180217049667005284, 496267460209336700111076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Fourth row of array A094416, which has more information.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Paul Barry, Three Études on a sequence transformation pipeline, arXiv:1803.06408 [math.CO], 2018.

FORMULA

E.g.f.: 1/(5 - 4*exp(x)).

a(n) = 4 * A050353(n) for n>0.

a(n) = Sum_{k, 0<=k<=n} A131689(n,k)*4^k. [Philippe Deléham, Nov 03 2008]

E.g.f.: A(x) with A_n = 4 * Sum_{k=0..n-1} C(n,k) * A_k; A_0 = 1. [Vladimir Kruchinin, Jan 27 2011]

G.f.: 2/G(0), where G(k)= 1 + 1/(1 - 8*x*(k+1)/(8*x*(k+1) - 1 + 10*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013

a(n) = log(5/4)*int {x = 0..inf} (floor(x))^n * (5/4)^(-x) dx. - Peter Bala, Feb 14 2015

MAPLE

a:= proc(n) option remember;

      `if`(n=0, 1, 4* add(binomial(n, k) *a(k), k=0..n-1))

    end:

seq(a(n), n=0..20);

MATHEMATICA

max = 16; f[x_] := 1/(5-4*E^x); CoefficientList[Series[f[x], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Nov 14 2011, after g.f. *)

PROG

(MAGMA) m:=20; R<x>:=LaurentSeriesRing(RationalField(), m); b:=Coefficients(R!(1/(5 - 4*Exp(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // Bruno Berselli, Mar 17 2014

CROSSREFS

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

Sequence in context: A197446 A291313 A002690 * A138435 A008546 A277404

Adjacent sequences:  A094414 A094415 A094416 * A094418 A094419 A094420

KEYWORD

nonn

AUTHOR

Ralf Stephan, May 02 2004

STATUS

approved

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Last modified November 19 08:40 EST 2018. Contains 317347 sequences. (Running on oeis4.)