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A229023
Numerators of the main diagonal of A225825 difference table, a sequence linked to Bernoulli, Genocchi and Clausen numbers.
1
1, -2, 16, -424, 2944, -70240, 70873856, -212648576, 98650550272, -90228445612544, 19078660567134208, -2034677178643867648, 123160010212358914048, -19182197131374977024, 228111332170536254898176, -51166426240975948419354886144
OFFSET
0,2
COMMENTS
a(n) is divisible by 2^n and congruent to 1, 2, 4, 5, 7 or 8 mod 9.
EXAMPLE
1, -2/3, 16/15, -424/105, 2944/105, -70240/231, 70873856/15015, ...
MATHEMATICA
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
CROSSREFS
Cf. A181131 (denominators), A225825, A110501 (Genocchi numbers), A141056 (Clausen numbers), A212196 (Bernoulli medians), A005439 (Genocchi medians).
Sequence in context: A343428 A282309 A009397 * A009700 A358784 A012030
KEYWORD
frac,sign,easy
AUTHOR
STATUS
approved