A335618 E.g.f.: Sum_{n>=0} Product_{k=1..n} tan(2*k*x).

1, 2, 16, 304, 10496, 568832, 44486656, 4742354944, 660908343296, 116642430451712, 25425572550148096, 6708171660023824384, 2106760489114215120896, 776654121137653931835392, 332101031506139993274843136, 163037618505293422657351450624, 91075662529714266445615040823296

Offset: 0

Author

Vaclav Kotesovec, Oct 02 2020

Keywords

• nonn

Crossrefs

Cf. A006752, A177382.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Sum[Product[Tan[2*k*x], {k, 1, n}], {n, 0, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) ~ 2^(n - 1/2) * n!^2 / G^(n+1), where G is the Catalan constant A006752.

a(n) = 2^n * A177382(n).