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Floor of the even-indexed Bernoulli numbers B_{2n} = A000367(n)/A002445(n).
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%I #21 Feb 27 2024 03:02:27

%S 1,0,-1,0,-1,0,-1,1,-8,54,-530,6192,-86581,1425517,-27298232,

%T 601580873,-15116315768,429614643061,-13711655205089,488332318973593,

%U -19296579341940069,841693047573682615,-40338071854059455414,2115074863808199160560,-120866265222965259346028

%N Floor of the even-indexed Bernoulli numbers B_{2n} = A000367(n)/A002445(n).

%D C. J. Moreno and S. S. Wagstaff, Jr., Sums of Squares of Integers, Chapman & Hall, 2006, p. 107.

%F a(n) = floor(B_(2n)), n>=0, with B_{2n} = A000367(n)/A002445(n) = A027641(2n)/A027642(2n).

%e n=4: B_8=-1/30=-0,033... hence a(4)=-1.

%t Floor@BernoulliB[2 Range[0, 20]] (* _Vladimir Reshetnikov_, Nov 12 2015 *)

%o (PARI) vector(30, n, n--; floor(bernfrac(2*n))) \\ _Altug Alkan_, Nov 12 2015

%Y Cf. A000367, A002445, A014509, A027641, A027642.

%K sign,easy

%O 0,9

%A _Wolfdieter Lang_, Nov 13 2007