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A101927 E.g.f. of sin(arcsinh(x)) = cos(arccosh(x)) (odd powers only). 4
1, -2, 20, -520, 26000, -2132000, 260104000, -44217680000, 9993195680000, -2898026747200000, 1049085682486400000, -463695871658988800000, 245758811979264064000000, -153845016299019304064000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Absolute values are expansion of sinh(arcsin(x)).

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..100

FORMULA

E.g.f.: sin(arcsinh(x)) =  x*sqrt(1+x^2)*(1 - 5*x^2/(G(0) + 5*x^2))) ; G(k) = (2*k+2)*(2*k+3) - x^2*(4*k^2+8*k+5) + x^2*(2*k+2)*(2*k+3)*(4*k^2+16*k+17)/G(k+1);

for sinh(arcsin(x)) = x*sqrt(1-x^2)*(1 + 5*x^2/(G(0) - 5*x^2))); G(k) = (2*k+2)*(2*k+3) + x^2*(4*k^2+8*k+5) - x^2*(2*k+2)*(2*k+3)*(4*k^2+16*k+17)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Dec 19 2011

G.f.: 1 + x*(G(0) - 1)/(x-1) where G(k) = 1 + (4*k^2+4*k+2)/(1-x/(x - 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 15 2013.

a(n) ~ (-1)^(n+1) * cosh(Pi/2) * 2^(2*n-1) * n^(2*n-2) / exp(2*n). - Vaclav Kotesovec, Oct 23 2013

EXAMPLE

sin(arcsinh(x)) = x - 2x^3/3! + 20x^5/5! - 520x^7/7! + 26000x^9/9! - ...

MAPLE

seq(coeff(series(factorial(n)*sin(arcsinh(x)), x, n+1), x, n), n=1..30, 2); # Muniru A Asiru, Jul 22 2018

MATHEMATICA

Table[n!*SeriesCoefficient[Sin[ArcSinh[x]], {x, 0, n}], {n, 1, 40, 2}] (* Vaclav Kotesovec, Oct 23 2013 *)

CROSSREFS

Bisection of A006228.

Sequence in context: A103353 A009344 A009699 * A157317 A009399 A275779

Adjacent sequences:  A101924 A101925 A101926 * A101928 A101929 A101930

KEYWORD

sign

AUTHOR

Ralf Stephan, Dec 28 2004

STATUS

approved

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Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)