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%I #12 May 14 2017 12:33:35
%S 1,-2,16,-424,2944,-70240,70873856,-212648576,98650550272,
%T -90228445612544,19078660567134208,-2034677178643867648,
%U 123160010212358914048,-19182197131374977024,228111332170536254898176,-51166426240975948419354886144
%N Numerators of the main diagonal of A225825 difference table, a sequence linked to Bernoulli, Genocchi and Clausen numbers.
%C a(n) is divisible by 2^n and congruent to 1, 2, 4, 5, 7 or 8 mod 9.
%e 1, -2/3, 16/15, -424/105, 2944/105, -70240/231, 70873856/15015, ...
%t nmax = 30; Clausen[n_] := Times @@ Select[Divisors[n] + 1, PrimeQ]; t = Join[{1}, Table[Numerator[BernoulliB[n, 1/2] - (n + 1)*EulerE[n, 0]]/Clausen[n], {n, 1, nmax}]]; dt = Table[Differences[t, n], {n, 0, nmax}]; Diagonal[dt] // Numerator
%Y Cf. A181131 (denominators), A225825, A110501 (Genocchi numbers), A141056 (Clausen numbers), A212196 (Bernoulli medians), A005439 (Genocchi medians).
%K frac,sign,easy
%O 0,2
%A _Jean-François Alcover_ and _Paul Curtz_, Sep 11 2013
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