A363152 a(n) = denominator(Sum_{j=0..2*n} Bernoulli(j, 1) * Bernoulli(2*n - j, 1)).

1, 12, 180, 630, 2100, 3465, 6306300, 30030, 2187900, 101846745, 355655300, 133855722, 121808707020, 10140585, 194090796900, 46329473220030, 4870754760300, 300840735195, 384913687052594700, 2473579378270, 100402586963979300, 27473798796507063, 17194486321623468

Offset

0,2

Comments

Conjecture: a(n) is cubefree. (An integer is cubefree if it is not divisible by the cube of a prime number.)

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = A363151(2*n).

Example

r(n) = 1, 7/12, -7/180, 23/630, -121/2100, 481/3465, -3015581/6306300, 67337/30030, ...

Maple

A363152 := n -> denom(add(bernoulli(j)*bernoulli(2*n - j), j = 0..2*n));
seq(A363152(n), n = 0..22);

Mathematica

Table[Denominator[Sum[BernoulliB[j, 1] * BernoulliB[2*n-j, 1], {j, 0, 2*n}]], {n, 0, 20}] (* Vaclav Kotesovec, May 19 2023 *)

Crossrefs

Cf. A363153 (numerator), A164555/A027642 (Bernoulli), A363150/A363151.

Sequence in context: A045952 A227714 A358951 * A350541 A130550 A073975

Adjacent sequences: A363149 A363150 A363151 * A363153 A363154 A363155

Keyword

nonn,frac

Author

Peter Luschny, May 18 2023

Status

approved