A273196 a(n) = numerator 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, -1, 37, -6833, 56377, -439772603, 27217772209, -202070742359, 80837575181815013, -155957202651688954367, 1770963292969902374951, -16092436217742770647634507, 2975968726866580246152132993, -963399772945511487665759472653, 3891037048609240492066339458106680163

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..14.

Mathematica

Table[Function[{n, m}, If[n == 0, 1, Numerator@ 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, 14}] (* Michael De Vlieger, Jun 26 2016 *)

Prog

(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).numerator()
print([a(n) for n in (0..14)])

Crossrefs

Cf. A273197 (denominator), T(n,0) = A000027, T(n,1) = A027641/A027642.

Also T(n,1)*(1*n+1)! = A129814, T(n,2)*(2*n+1)! = A273198.

Sequence in context: A221498 A296687 A297653 * A131272 A219105 A219984

Adjacent sequences: A273193 A273194 A273195 * A273197 A273198 A273199

Keyword

sign,frac

Author

Peter Luschny, Jun 26 2016

Status

approved