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a(n) = numerator(Sum_{k=1..2*n} Bernoulli(1 + k) / ((1 + k) * k^(1 + k))).
2

%I #10 Aug 13 2021 06:36:44

%S 0,1,809,17696929,29148363745769,13802156299837263870439,

%T 51192911535225069982129975520643227,

%U 15505058537999075182938597423297191148526445182931,25740819838475027138304706528711851561870640774224535090837

%N a(n) = numerator(Sum_{k=1..2*n} Bernoulli(1 + k) / ((1 + k) * k^(1 + k))).

%t r[n_] := Sum[BernoulliB[1 + k] / ((1 + k) * k^(1 + k)), {k, 1, 2*n}];

%t Table[r[n], {n, 0, 10}] // Numerator

%o (PARI) a(n) = numerator(sum(k=1, 2*n, bernfrac(1+k)/((1+k)*k^(1+k)))); \\ _Michel Marcus_, Aug 12 2021

%Y Cf. A346717 (denominator), A346718 (rational limit).

%K nonn,frac

%O 0,3

%A _Peter Luschny_, Aug 11 2021