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%I #9 Sep 14 2013 03:12:11
%S 1,7,11,7,19,337,5,-1681,22133,-87223,427291,-118181363,4276553,
%T -11874730297,4307920641583,-3854660520481,1288843929185,
%U -13157635776526258889,1464996956920781,-130541359248224557643
%N Bisection of A195240(n).
%C The first bisection is b(n) = 0, 1, 8, 10, 8, 14, 1028, -2, 1936, -21734,... .
%C a(n) and b(n) are twice linked to Bernoulli numbers (A027641(n+4) or A164555(n+4))/A027642(n+4).
%F A195240(2n+1).
%F a(n+1) = b(n+2) + A000367(n+2).
%F a(n+1) = A001897(n+2) - b(n+2).
%F 2*a(n+1) = A000367(n+2) + A001897(n+2).
%t evb = Join[{0, 1, 0}, Table[BernoulliB[n], {n, 2, 42}]]; ievb = Table[ Sum[Binomial[n, k]*evb[[k + 1]], {k, 0, n}], {n, 0, Length[evb] - 3}]; A195240 = Differences[ievb, 2] // Numerator; Partition[A195240, 2][[All, 2]]
%t (* or *)
%t A000367[n_] := BernoulliB[2*n] // Numerator; A001897[n_] := -2*(2^(2*n - 1) - 1)*BernoulliB[2*n] // Denominator; a[0] = 1; a[n_] := (A000367[n + 1] + A001897[n + 1])/2; Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Sep 09 2013, after R. J. Mathar *)
%K sign
%O 0,2
%A _Paul Curtz_, Sep 09 2013
%E More terms from _Jean-François Alcover_, Sep 09 2013
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