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A151919
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a(n) = (-2)^n*A_{n,3}(1/2) where A_{n,k}(x) are the generalized Eulerian polynomials.
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8
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1, -4, 34, -442, 7654, -165634, 4301254, -130313362, 4512058774, -175757170114, 7606919927974, -362157366660082, 18809374928573494, -1058311485335621794, 64126470727596628294, -4163172358878650459602, 288297029592971540217814, -21212159439736738874060674
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: exp(-x)/(2 - exp(-3*x)). (see e.g.f. of row sums of A284861 with x -> -x). - Wolfdieter Lang, Jul 12 2017
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MATHEMATICA
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m = 18; CoefficientList[Exp[-x]/(2 - Exp[-3x]) + O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Jun 19 2019 *)
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PROG
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(SageMath)
@CachedFunction
def BB(n, k, x): # modified cardinal B-splines
if n == 1: return 0 if (x < 0) or (x >= k) else 1
return x*BB(n-1, k, x) + (n*k-x)*BB(n-1, k, x-k)
def EulerianPolynomial(n, k, x):
if n == 0: return 1
return add(BB(n+1, k, k*m+1)*x^m for m in (0..n))
[(-2)^n*EulerianPolynomial(n, 3, 1/2) for n in (0..17)]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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