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A295257
Expansion of e.g.f. cot(x)*(1 - sqrt(1 - 4*tan(x)))/2.
6
1, 1, 4, 32, 368, 5656, 109024, 2533712, 68995328, 2155513216, 76014982144, 2987332904192, 129473128921088, 6135478762187776, 315609465774936064, 17515027337549545472, 1043104219010147483648, 66358462250378681614336, 4491141928841064201846784, 322219449242531127348887552
OFFSET
0,3
LINKS
FORMULA
E.g.f.: 1/(1 - tan(x)/(1 - tan(x)/(1 - tan(x)/(1 - tan(x)/(1 - ...))))), a continued fraction.
a(n) ~ sqrt(17/2) * n^(n-1) / (exp(n) * (arctan(1/4))^(n-1/2)). - Vaclav Kotesovec, Nov 18 2017
MAPLE
S:= series(cot(x)*(1 - sqrt(1 - 4*tan(x)))/2, x, 32):
seq(n!*coeff(S, x, n), n=0..30); # Robert Israel, Nov 18 2017
MATHEMATICA
nmax = 19; CoefficientList[Series[Cot[x] (1 - Sqrt[1 - 4 Tan[x]])/2, {x, 0, nmax}], x] Range[0, nmax]!
nmax = 19; CoefficientList[Series[1/(1 + ContinuedFractionK[-Tan[x], 1, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 18 2017
STATUS
approved