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A024263 Expansion of sinh(tan(x)*x)/2. 2
0, 1, 4, 108, 4448, 276560, 24034752, 2782112704, 413640580096, 76768625740032, 17380983003345920, 4711153236657376256, 1505098422997799215104, 559357234754573189828608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit n->infinity A024263(n)/A009252(n) = 1/4. - Vaclav Kotesovec, Jan 20 2015

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..238

FORMULA

a(n) ~ n^(2*n-1/4) * 2^(4*n-7/4) * exp(2*sqrt(2*n)-2*n-1/2) / Pi^(2*n) * (1 - (Pi^2-1)/(12*sqrt(2*n))). - Vaclav Kotesovec, Jan 20 2015

MATHEMATICA

Sinh[ Tan[ x ]*x ]/2 (* Even Part *)

With[{nn=40}, Take[CoefficientList[Series[Sinh[Tan[x]*x]/2, {x, 0, nn}], x] * Range[0, nn]!, {1, -1, 2}]] (* Vaclav Kotesovec, Jan 20 2015 *)

CROSSREFS

Cf. A009252, A009611.

Sequence in context: A336028 A131092 A123056 * A090205 A061464 A107048

Adjacent sequences:  A024260 A024261 A024262 * A024264 A024265 A024266

KEYWORD

nonn

AUTHOR

R. H. Hardin

EXTENSIONS

Extended and signs tested 03/97.

STATUS

approved

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Last modified August 16 05:38 EDT 2022. Contains 356162 sequences. (Running on oeis4.)