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A027648
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Denominators of poly-Bernoulli numbers B_n^(k) with k=4.
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6
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1, 16, 1296, 3456, 3240000, 144000, 1555848000, 59270400, 5000940000, 1587600, 9762501672000, 11269843200, 221794053611130000, 39390663312000, 5849513501832000, 519437318400, 407131014322092060000, 1063331477208000
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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 = 4.
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MAPLE
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a:= (n, k) -> denom( (-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[Denominator@ 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)
A027648:= func< n, k | Denominator( (&+[(-1)^(j+n)*Factorial(j)*StirlingSecond(n, j)/(j+1)^k: j in [0..n]]) ) >;
(SageMath)
def A027648(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,easy
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AUTHOR
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STATUS
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approved
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