A363153 a(n) = numerator(Sum_{j=0..2*n} Bernoulli(j, 1) * Bernoulli(2*n - j, 1)).

1, 7, -7, 23, -121, 481, -3015581, 67337, -30135767, 10946836702, -369658793327, 1633542173485, -20836336617617359, 28614002185051, -10503257306519121539, 55315660282703717655037, -146269786633489194137851, 256962811799649370068488, -10500086267327643941391664345141

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = A363150(2*n).

Example

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

Maple

A363153 := n -> numer(add(bernoulli(j)*bernoulli(2*n - j), j = 0..2*n)):
seq(A363153(n), n = 0..18);

Mathematica

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

Crossrefs

Cf. A363152 (denominator), A164555/A027642 (Bernoulli), A363150/A363151.

Sequence in context: A289378 A289409 A290520 * A247666 A255279 A230496

Adjacent sequences: A363150 A363151 A363152 * A363154 A363155 A363156

Keyword

sign,frac

Author

Peter Luschny, May 18 2023

Status

approved