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A027644
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Denominators of poly-Bernoulli numbers B_n^(k) with k=2.
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6
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1, 4, 36, 24, 450, 40, 2205, 168, 350, 120, 38115, 88, 40990950, 10920, 5005, 24, 130180050, 136, 1935088155, 3192, 177827650, 1320, 1539340803, 184, 304521767550, 10920, 37182145, 24, 2814316555050, 1160
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OFFSET
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0,2
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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) = denominator of Sum_{j=0..n} (-1)^(n+j) * j! * Stirling2(n, j) * (j+1)^(-k), for k = 2.
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MAPLE
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a := n -> denom(add((-1)^(n-m)*m!*Stirling2(n, m)/(m+1)^2, m=0..n)):
seq(a(n), n = 0..29);
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MATHEMATICA
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f[n_]:= (-1)^n*Sum[(-1)^m*m!*StirlingS2[n, m]/(m + 1)^2, {m, 0, n}];
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PROG
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(Magma)
A027644:= func< n, k | Denominator( (&+[(-1)^(j+n)*Factorial(j)*StirlingSecond(n, j)/(j+1)^k: j in [0..n]]) ) >;
(SageMath)
def A027644(n, k): return denominator( 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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nonn,frac
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AUTHOR
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STATUS
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approved
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