A357594 Expansion of e.g.f. log(1-x) * tan(log(1-x)/2).

0, 0, 1, 3, 12, 60, 362, 2562, 20820, 191088, 1955020, 22061380, 272197160, 3645227040, 52656804440, 816114251400, 13508168448400, 237805776169600, 4436759277524400, 87445191383773200, 1815460566861236000, 39600109151685600000, 905416958295793788000

Offset

0,4

Links

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

Formula

a(n) = 2 * Sum_{k=0..floor(n/2)} (-1)^k * (1-4^k) * |Stirling1(n,2*k)| * Bernoulli(2*k).

a(n) ~ n! * 2*Pi / (exp(Pi) * (1 - exp(-Pi))^(n+1)). - Vaclav Kotesovec, Oct 05 2022

Prog

(PARI) my(N=30, x='x+O('x^N)); concat([0, 0], Vec(serlaplace(log(1-x)*tan(log(1-x)/2))))
(PARI) a(n) = 2*sum(k=0, n\2, (-1)^k*(1-4^k)*abs(stirling(n, 2*k, 1))*bernfrac(2*k));

Crossrefs

Cf. A136128, A357591.

Sequence in context: A105752 A177138 A053532 * A159867 A082278 A078162

Adjacent sequences: A357591 A357592 A357593 * A357595 A357596 A357597

Keyword

nonn

Author

Seiichi Manyama, Oct 05 2022

Status

approved