A330906 Denominator of 1/Pi^(4*n+3) * Sum_{k>0} (-1)^(k+1) / (k^(4*n+3) * sinh(Pi * k)).

360, 453600, 13621608000, 4547140416000, 844351508246400000, 2481187700290640140800000, 4625642784113264833920000000, 72771380848009396571232614400000000, 121040492221732333298138065066291200000000, 4859044199288026228257452368062289920000000000

Offset

0,1

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

MathStackexchange, A Ramanujan sum involving sinh

Wikipedia, Bernoulli number

Formula

Let B_n be the Bernoulli number.

A330905(n)/a(n) = Sum_{k=0..2*n+2} (-1)^k*(1-2^(2*k-1))*(1-2^(4*n+3-2*k))*B_{2*k}*B_{4*n+4-2*k}/((2*k)!*(4*n+4-2*k)!)).

Mathematica

a[n_] := Denominator[Sum[(-1)^k * (1 - 2^(2*k - 1)) * (1 - 2^(4*n + 3 - 2*k)) * BernoulliB[2*k] * BernoulliB[4*n + 4 - 2*k]/((2*k)!*(4*n + 4 - 2*k)!), {k, 0, 2*n + 2}]]; Array[a, 10, 0] (* Amiram Eldar, May 01 2020 *)

Prog

(PARI) {a(n) = denominator(sum(k=0, 2*n+2, (-1)^k*(1-2^(2*k-1))*(1-2^(4*n+3-2*k))*bernfrac(2*k)*bernfrac(4*n+4-2*k)/((2*k)!*(4*n+4-2*k)!)))}

Crossrefs

Cf. A004767, A057866/A057867, A330905 (numerator).

Sequence in context: A145412 A156032 A295452 * A003799 A003930 A137607

Adjacent sequences: A330903 A330904 A330905 * A330907 A330908 A330909

Keyword

nonn,frac

Author

Seiichi Manyama, May 01 2020

Status

approved