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A027647
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Numerators of poly-Bernoulli numbers B_n^(k) with k=4.
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5
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1, 1, -49, 41, 26291, -1921, 845233, 1048349, -60517579, -50233, 506605371959, 823605863, -53797712101337483, -7784082036337, 8049010408144441, 246319059461, -3910018782537447618421, 1090400590625849
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OFFSET
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0,3
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LINKS
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Masanobu Kaneko, Poly-Bernoulli numbers, Journal de théorie des nombres de Bordeaux, 9 no. 1 (1997), Pages 221-228.
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FORMULA
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a(n) = numerator of Sum_{j=0..n} (-1)^(n+j) * j! * Stirling2(n, j) * (j+1)^(-k), for k = 4.
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MAPLE
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a:= (n, k)-> numer((-1)^n*add((-1)^m*m!*Stirling2(n, m)/(m+1)^k, m=0..n)):
seq(a(n, 4), n = 0..30);
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MATHEMATICA
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With[{k = 4}, Table[Numerator@ Sum[((-1)^(m + n))*m!*StirlingS2[n, m]*(m + 1)^(-k), {m, 0, n}], {n, 0, 17}]] (* Michael De Vlieger, Mar 18 2017 *)
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PROG
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(Magma)
A027647:= func< n, k | Numerator( (&+[(-1)^(j+n)*Factorial(j)*StirlingSecond(n, j)/(j+1)^k: j in [0..n]]) ) >;
(SageMath)
def A027647(n, k): return numerator( sum((-1)^(n+j)*factorial(j)*stirling_number2(n, j)/(j+1)^k for j in (0..n)) )
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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