A273197 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) ).

1, 3, 15, 105, 15, 1155, 455, 15, 19635, 95095, 2145, 31395, 7735, 2805, 10818885, 50115065, 3315, 596505, 80925845, 3795, 18515805, 221847535, 2211105, 204920500785, 1453336885, 148335, 95055765, 287558635, 27897511785, 397299047145, 5613813089885, 8897205

Offset: 0

Author

Peter Luschny, Jun 26 2016

Keywords

• nonn
• frac

Comments

T(n,0) are the natural numbers, T(n,1) the Bernoulli numbers.

Crossrefs

Cf. A273196 (numerators).

T(n,0) = A000027(n) for n>=1.

T(n,1) = A027641(n)/A027642(n) for all n>=0.

T(n,1)*(1*n+1)! = A129814(n) for all n>=0.

T(n,2)*(2*n+1)! = A273198(n) for all n>=0.

Programs

Mathematica

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 *)

Sage

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))
def a(n): return T(n, 2).denominator()
print([a(n) for n in (0..31)])