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%I #19 Mar 08 2020 10:14:19
%S 1,3,15,105,15,1155,455,15,19635,95095,2145,31395,7735,2805,10818885,
%T 50115065,3315,596505,80925845,3795,18515805,221847535,2211105,
%U 204920500785,1453336885,148335,95055765,287558635,27897511785,397299047145,5613813089885,8897205
%N a(n) = denominator of T(n, 2) with T(n, m) = Sum_{k=0..n}( 1/(m*k+1) * Sum_{j=0..m*k} (-1)^j*C(k,j)*j^(m*n) ).
%C T(n,0) are the natural numbers, T(n,1) the Bernoulli numbers.
%t Table[Function[{n, m}, If[n == 0, 1, Denominator@ Sum[1/(m k + 1) Sum[(-1)^j Binomial[k, j] j^(m n), {j, 0, m k}], {k, 0, n}]]][n, 2], {n, 0, 31}] (* _Michael De Vlieger_, Jun 26 2016 *)
%o (Sage)
%o def T(n, m): return sum(1/(m*k+1)*sum((-1)^j*binomial(k,j)*j^(m*n) for j in (0..m*k)) for k in (0..n))
%o def a(n): return T(n, 2).denominator()
%o print([a(n) for n in (0..31)])
%Y Cf. A273196 (numerators).
%Y T(n,0) = A000027(n) for n>=1.
%Y T(n,1) = A027641(n)/A027642(n) for all n>=0.
%Y T(n,1)*(1*n+1)! = A129814(n) for all n>=0.
%Y T(n,2)*(2*n+1)! = A273198(n) for all n>=0.
%K nonn,frac
%O 0,2
%A _Peter Luschny_, Jun 26 2016
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