A363151 a(n) = denominator(Sum_{j=0..n} Bernoulli(j, 1) * Bernoulli(n - j, 1)).

1, 1, 12, 6, 180, 30, 630, 42, 2100, 30, 3465, 66, 6306300, 2730, 30030, 6, 2187900, 510, 101846745, 798, 355655300, 330, 133855722, 138, 121808707020, 2730, 10140585, 6, 194090796900, 870, 46329473220030, 14322, 4870754760300, 510, 300840735195, 6, 384913687052594700

Offset

0,3

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..36.

Formula

Let r(n) denote the rational form of this sequence.

r(2*n + 1) = A164555(2*n)/A027642(2*n) = Bernoulli(2*n, 1).

r(2*n) = A363153(n)/A363152(n).

Example

r(n) = 1, 1, 7/12, 1/6, -7/180, -1/30, 23/630, 1/42, -121/2100, -1/30, 481/3465, 5/66, ...

Maple

A363151 := n -> denom(add(bernoulli(j, 1) * bernoulli(n - j, 1), j = 0..n)):
seq(A363151(n), n = 0..36);

Mathematica

Table[Denominator[Sum[BernoulliB[j, 1] * BernoulliB[n-j, 1], {j, 0, n}]], {n, 0, 30}] (* Vaclav Kotesovec, May 19 2023 *)

Crossrefs

Cf. A363150 (numerator), A164555/A027642 (Bernoulli), A363153/A363152.

Sequence in context: A038332 A093763 A002548 * A359632 A364135 A305939

Adjacent sequences: A363148 A363149 A363150 * A363152 A363153 A363154

Keyword

nonn,frac

Author

Peter Luschny, May 18 2023

Status

approved