A306821 Inverse binomial transform of the "original" Bernoulli numbers [A164555(n)/A027642(n)] with 1 and 1/2 swapped. Denominators.

2, 2, 3, 1, 15, 1, 21, 1, 15, 1, 33, 1, 1365, 1, 3, 1, 255, 1, 399, 1, 165, 1, 69, 1, 1365, 1, 3, 1, 435, 1, 7161, 1, 255, 1, 3, 1, 959595, 1, 3, 1, 6765, 1, 903, 1, 345, 1, 141, 1, 23205, 1, 33, 1, 795, 1, 399, 1

Offset

0,1

Comments

Fractions: 1/2, 1/2, -4/3, 2, -38/15, 3, -73/21, 4, -68/15, 5, -179/33, 6, -9218/1365, 7, ... .

Numerators are A307974(n).

a(2n) same as denominators of cosecant numbers A001897 for n>0 (conjectured).

Links

Table of n, a(n) for n=0..55.

Formula

a(n) = A141459(n) * A141044(n).

a(n) = A141459(n) for n>2.

a(2n+1) = A054977(n).

a(2n) = A001897(n) * A054977(n).

Mathematica

b[n_] = BernoulliB[n]; b[0] = 1/2; b[1] = 1;
a[n_] := Sum[(-1)^(n - k)*Binomial[n, k]*b[k], {k, 0, m}] // Denominator;
Table[a[n], {n, 0, 55}] (* Jean-François Alcover, Jun 04 2019 *)

Crossrefs

Essentially the same as A141459.

Cf. A001897, A027642, A054977, A141044, A164555, A307974.

Sequence in context: A273218 A173160 A022461 * A271226 A292372 A098008

Adjacent sequences: A306818 A306819 A306820 * A306822 A306823 A306824

Keyword

nonn,frac

Author

Paul Curtz, Jun 04 2019

Status

approved