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A296839 Expansion of e.g.f. tan(x*tan(x/2)) (even powers only). 10
0, 1, 1, 33, 437, 22205, 978873, 81005113, 7356832669, 949918117653, 142805534055905, 27120922891214801, 6016195462632487941, 1592800634594574194413, 486576430503128985793417, 171866951067212728072402665, 69025662074064538734826793453 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

FORMULA

a(n) = (2*n)! * [x^(2*n)] tan(x*tan(x/2)).

a(n) ~ c * d^n * n^(2*n + 1/2) / exp(2*n), where d = 1.621138938277404343102071411355642222469740394755... is the root of the equation tan(1/sqrt(d)) = Pi*sqrt(d)/4 and c = 1.75568815831... - Vaclav Kotesovec, Dec 21 2017

EXAMPLE

tan(x*tan(x/2)) = x^2/2! + x^4/4! + 33*x^6/6! + 437*x^8/8! + ...

MATHEMATICA

nmax = 16; Table[(CoefficientList[Series[Tan[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]

CROSSREFS

Cf. A000182, A001469, A003718, A009707, A024265, A110501, A296835, A296841, A296842.

Sequence in context: A252925 A107965 A220591 * A296988 A058796 A214144

Adjacent sequences:  A296836 A296837 A296838 * A296840 A296841 A296842

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 21 2017

STATUS

approved

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)