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a(n) = numerator of Bernoulli(2*n)/(2*n + 1)!. Bisection of A120082.
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%I #39 Sep 16 2024 05:57:57

%S 1,1,-1,1,-1,1,-691,1,-3617,43867,-174611,77683,-236364091,657931,

%T -3392780147,1723168255201,-7709321041217,151628697551,

%U -26315271553053477373,154210205991661,-261082718496449122051,1520097643918070802691,-2530297234481911294093

%N a(n) = numerator of Bernoulli(2*n)/(2*n + 1)!. Bisection of A120082.

%C Numerators of the Taylor expansion coefficients of the Debye function D(1,x) at the even powers of x.

%H Peter Luschny, <a href="/A141590/b141590.txt">Table of n, a(n) for n = 0..300</a>

%H Kevin Acres and David Broadhurst, <a href="https://arxiv.org/1810.07478">Eta quotients and Rademacher sums</a>, arXiv:1810.07478 [math.NT], 2018.

%F a(n) = A120082(2*n).

%e Note that a(34) = -125235502160125163977598011460214000388469 but A255505(34) = -4633713579924631067171126424027918014373353.

%p A141590 := proc(n) A120082(2*n) end:

%p seq(A141590(n), n=0..30) ; # _R. J. Mathar_, Sep 03 2009

%p seq(numer(bernoulli(2*n)/(2*n+1)!), n=0..34); # _Peter Luschny_, Dec 03 2022

%t Table[Numerator[BernoulliB[2*n]/(2*n+1)!], {n,0,35}] (* _G. C. Greubel_, Sep 16 2024 *)

%o (Magma)

%o A141590:= func< n | Numerator(BernoulliNumber(2*n)/Factorial(2*n+1)) >;

%o [A141590(n): n in [0..35]]; // _G. C. Greubel_, Sep 16 2024

%o (SageMath)

%o def A141590(n): return numerator(bernoulli(2*n)/factorial(2*n+1))

%o [A141590(n) for n in range(36)] # _G. C. Greubel_, Sep 16 2024

%Y Cf. A000367, A001067, A046968, A120082, A255505.

%K sign,frac

%O 0,7

%A _Paul Curtz_, Aug 20 2008

%E Edited and extended by _R. J. Mathar_, Sep 03 2009

%E Edited by _Peter Luschny_, Dec 03 2022