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A119884
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Expansion of e.g.f. sech(x)/(1-x).
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1
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1, 1, 1, 3, 17, 85, 449, 3143, 26529, 238761, 2337089, 25707979, 311198513, 4045580669, 56438768385, 846581525775, 13564695924545, 230599830717265, 4148392073235329, 78819449391471251, 1576759359017662545
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OFFSET
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0,4
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COMMENTS
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Transform of n! under the matrix A119879.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} A119879(n,k) * k!.
E.g.f.: 1/U(0) where U(k) = 1 - x/(1 - x/(x - (2*k+1)*(2*k+2)/U(k+1)); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 17 2012
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MAPLE
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restart: G(x):= sech(x)/(1-x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # Zerinvary Lajos, Apr 03 2009
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MATHEMATICA
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CoefficientList[Series[1/((1-x)*(E^x/2+E^(-x)/2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)
Table[n!*Sum[EulerE[j]/j!, {j, 0, n}], {n, 0, 40}] (* G. C. Greubel, Jun 07 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( 1/((1-x)*Cosh(x)) ))); // G. C. Greubel, Jun 07 2023
(SageMath)
def A119884(n): return factorial(n)*sum(euler_number(j)/factorial(j) for j in range(n+1))
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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