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A094417
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Generalized ordered Bell numbers Bo(4,n).
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18
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1, 4, 36, 484, 8676, 194404, 5227236, 163978084, 5878837476, 237109864804, 10625889182436, 523809809059684, 28168941794178276, 1641079211868751204, 102961115527874385636, 6921180217049667005284, 496267460209336700111076
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OFFSET
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0,2
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COMMENTS
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Fourth row of array A094416, which has more information.
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LINKS
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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.
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FORMULA
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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
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MAPLE
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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);
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MATHEMATICA
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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. *)
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PROG
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(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
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CROSSREFS
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Cf. A000670, A004123, A032033, A094418, A094419.
Sequence in context: A197446 A291313 A002690 * A349504 A354264 A138435
Adjacent sequences: A094414 A094415 A094416 * A094418 A094419 A094420
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, May 02 2004
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STATUS
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approved
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