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A343206
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Numerators of Daehee numbers.
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3
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1, -1, 2, -3, 24, -20, 720, -630, 4480, -36288, 3628800, -3326400, 479001600, -444787200, 5811886080, -81729648000, 20922789888000, -19760412672000, 6402373705728000, -6082255020441600, 115852476579840000, -2322315553259520000, 1124000727777607680000, -1077167364120207360000
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OFFSET
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0,3
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LINKS
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FORMULA
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D(n) = Sum_{i=0..n} Stirling1(n, i)*Bernoulli(i).
E.g.f. for D(n): log(1+x)/x.
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EXAMPLE
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1, -1/2, 2/3, -3/2, 24/5, -20, 720/7, -630, 4480, -36288, 3628800/11, -3326400, 479001600/13, -444787200, ...
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MATHEMATICA
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a[n_]:=Numerator[(-1)^n*n!/(n+1)]; Array[a, 24, 0] (* Stefano Spezia, Jun 24 2024 *)
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PROG
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(PARI) a(n) = numerator(sum(i=0, n, stirling(n, i, 1)*bernfrac(i)));
(PARI) my(x='x+O('x^30), v=Vec(serlaplace(log(1+x)/x))); apply(numerator, v)
(Python)
from sympy.functions.combinatorial.numbers import stirling, bernoulli
def A343206(n): return sum(stirling(n, i, signed=True)*bernoulli(i) for i in range(n+1)).p # Chai Wah Wu, Apr 08 2021
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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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