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%I #17 May 19 2023 13:06:26
%S 1,1,12,6,180,30,630,42,2100,30,3465,66,6306300,2730,30030,6,2187900,
%T 510,101846745,798,355655300,330,133855722,138,121808707020,2730,
%U 10140585,6,194090796900,870,46329473220030,14322,4870754760300,510,300840735195,6,384913687052594700
%N a(n) = denominator(Sum_{j=0..n} Bernoulli(j, 1) * Bernoulli(n - j, 1)).
%C Conjecture: a(n) is cubefree. (An integer is cubefree if it is not divisible by the cube of a prime number.)
%F Let r(n) denote the rational form of this sequence.
%F r(2*n + 1) = A164555(2*n)/A027642(2*n) = Bernoulli(2*n, 1).
%F r(2*n) = A363153(n)/A363152(n).
%e r(n) = 1, 1, 7/12, 1/6, -7/180, -1/30, 23/630, 1/42, -121/2100, -1/30, 481/3465, 5/66, ...
%p A363151 := n -> denom(add(bernoulli(j, 1) * bernoulli(n - j, 1), j = 0..n)):
%p seq(A363151(n), n = 0..36);
%t Table[Denominator[Sum[BernoulliB[j, 1] * BernoulliB[n-j, 1], {j,0,n}]], {n,0,30}] (* _Vaclav Kotesovec_, May 19 2023 *)
%Y Cf. A363150 (numerator), A164555/A027642 (Bernoulli), A363153/A363152.
%K nonn,frac
%O 0,3
%A _Peter Luschny_, May 18 2023
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