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A094417
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Generalized ordered Bell numbers Bo(4,n).
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3
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1, 4, 36, 484, 8676, 194404, 5227236, 163978084, 5878837476, 237109864804, 10625889182436, 523809809059684, 28168941794178276, 1641079211868751204, 102961115527874385636, 6921180217049667005284, 496267460209336700111076
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Fourth row of array A094416, which has for more information.
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FORMULA
| E.g.f.: 1/(5 - 4*exp(x)).
a(n) = Sum_{k, 0<=k<=n} A131689(n,k)*4^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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. [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), Jan 27 2011]
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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);
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MATHEMATICA
| max = 16; f[x_] := 1/(5-4*E^x); CoefficientList[ Series[ f[x], {x, 0, max}], x]*Range[0, max]! (* From Jean-François Alcover, Nov 14 2011, after g.f. *)
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CROSSREFS
| Equals 4 * A050353(n) for n>0.
Sequence in context: A135906 A197446 A002690 * A138435 A008546 A024253
Adjacent sequences: A094414 A094415 A094416 * A094418 A094419 A094420
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, May 02 2004
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