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%I #12 Jan 16 2024 04:08:46
%S -1,1,-1,10,-21,1050,-45606,6306300,-32585553,5332033850,
%T -646674981498,248655336029100,-579463114572870,400708622091878100,
%U -31790012531476579380,43435207772044760997000,-31514892593265599765292045,814247185935070977732893250
%N a(n) = Sum_{k=0..n} A369134(n, k).
%C See A369134 for comments.
%F a(n) / A369135(n) = Bernoulli(2*n).
%t A368846[n_, k_] := If[k == 0, Boole[n == 0], (-1)^(n + k) 2 Binomial[2 k - 1, n] Binomial[2 n + 1, 2 k]];
%t Map[Total[# LCM @@ Denominator[#]]&, MapIndexed[(-1)^First[#2] Take[#, First[#2]]&, Inverse[PadRight[Table[A368846[n, k], {n, 0, 20}, {k, 0, n}]]]]] (* _Paolo Xausa_, Jan 16 2024 *)
%Y Cf. A369134, A000367/A002445 (Bernoulli(2n)).
%K sign
%O 0,4
%A _Peter Luschny_, Jan 14 2024
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