A363150 a(n) = numerator(Sum_{j=0..n} Bernoulli(j, 1) * Bernoulli(n - j, 1)).

1, 1, 7, 1, -7, -1, 23, 1, -121, -1, 481, 5, -3015581, -691, 67337, 7, -30135767, -3617, 10946836702, 43867, -369658793327, -174611, 1633542173485, 854513, -20836336617617359, -236364091, 28614002185051, 8553103, -10503257306519121539, -23749461029

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Formula

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

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

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], ...
The numbers in square brackets are the Bernoulli numbers. Roughly speaking, in the Bernoulli sequence, one replaces the vanishing terms and B(1) with A363153/A363152 and then shifts the sequence one place to the right. For the exact description see the Formula section.

Maple

A363150 := n -> numer(add(bernoulli(j, 1) * bernoulli(n - j, 1), j = 0..n)):
seq(A363150(n), n = 0..28);

Mathematica

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

Crossrefs

Cf. A363151 (denominator), A164555/A027642 (Bernoulli), A363153/A363152.

Sequence in context: A010688 A176415 A356948 * A317846 A198219 A198580

Adjacent sequences: A363147 A363148 A363149 * A363151 A363152 A363153

Keyword

sign,frac

Author

Peter Luschny, May 18 2023

Status

approved