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a(n) = numerator(denominator(Bernoulli'(n, x)) / denominator(Bernoulli(n, 1))).
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%I #11 Oct 14 2023 13:12:16

%S 1,1,1,2,1,6,1,6,1,10,1,6,1,210,5,2,1,30,5,210,7,110,5,30,1,546,7,14,

%T 1,30,1,462,77,1190,35,6,1,51870,455,70,7,2310,55,2310,7,322,35,210,1,

%U 6630,221,286,11,330,55,798,19,290,5,30,1,930930,5005,1430

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

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

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

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

%Y Cf. A324370/A027642, A366152 (denominator), A366426/A366427 (2nd derivative).

%K nonn,frac

%O 0,4

%A _Peter Luschny_, Oct 13 2023