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a(n) = denominator(denominator(Bernoulli'(n, x)) / denominator(Bernoulli(n, 1))).
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%I #11 Oct 14 2023 13:12:07

%S 1,2,6,1,30,1,42,1,10,1,66,1,2730,1,2,1,170,1,798,1,110,1,46,1,546,1,

%T 2,1,870,1,14322,1,170,1,2,1,1919190,1,2,1,4510,1,1806,1,46,1,94,1,

%U 1326,1,22,1,530,1,798,1,290,1,118,1,56786730,1,2,1,34,1,64722

%N a(n) = denominator(denominator(Bernoulli'(n, x)) / denominator(Bernoulli(n, 1))).

%F a(n) = denominator(A324370(n) / A027642(n)).

%p seq(denom(denom(diff(bernoulli(n, x), x))/denom(bernoulli(n, 1))), n = 0..66);

%o (PARI) a(n) = denominator(lcm(apply(denominator, Vec(deriv(bernpol(n)))))/denominator(subst(bernpol(n, x), x, 1))); \\ _Michel Marcus_, Oct 14 2023

%Y Cf. A324370/A027642, A366570 (numerator), A366426/A366427 (2nd derivative).

%K nonn,frac

%O 0,2

%A _Peter Luschny_, Oct 13 2023