|
%I #10 May 19 2023 05:32:09
%S 1,12,180,630,2100,3465,6306300,30030,2187900,101846745,355655300,
%T 133855722,121808707020,10140585,194090796900,46329473220030,
%U 4870754760300,300840735195,384913687052594700,2473579378270,100402586963979300,27473798796507063,17194486321623468
%N a(n) = denominator(Sum_{j=0..2*n} Bernoulli(j, 1) * Bernoulli(2*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 a(n) = A363151(2*n).
%e r(n) = 1, 7/12, -7/180, 23/630, -121/2100, 481/3465, -3015581/6306300, 67337/30030, ...
%p A363152 := n -> denom(add(bernoulli(j)*bernoulli(2*n - j), j = 0..2*n));
%p seq(A363152(n), n = 0..22);
%t Table[Denominator[Sum[BernoulliB[j, 1] * BernoulliB[2*n-j, 1], {j,0,2*n}]], {n,0,20}] (* _Vaclav Kotesovec_, May 19 2023 *)
%Y Cf. A363153 (numerator), A164555/A027642 (Bernoulli), A363150/A363151.
%K nonn,frac
%O 0,2
%A _Peter Luschny_, May 18 2023
|
