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A012077
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tan(arcsin(tan(x))) = x+5/3!*x^3+121/5!*x^5+6845/7!*x^7+698161/9!*x^9...
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2
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1, 5, 121, 6845, 698161, 111973685, 25947503401, 8200346492525, 3389281372287841, 1774459993676715365, 1147649139272698443481, 898537335398420151634205, 837511978485668107020082321
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history;
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internal format)
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OFFSET
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0,2
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LINKS
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Robert Israel, Table of n, a(n) for n = 0..215
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FORMULA
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a(n) = Sum_(m=0..n, binomial(2*m,m)*Sum_(j=0..2*n-2*m, binomial(j+2*m,2*m)*(j+2*m+1)!*2^(2*n-j-4*m)*(-1)^(n+m+j)*stirling2(2*n+1,j+2*m+1))) /((2*n+1)!), n>0. - Vladimir Kruchinin, Jun 15 2011
From Peter Luschny, May 13 2017 (Start)
a(n) = (2*n+1)! [x^(2*n+1)] tan(x)/sqrt(1-tan(x)^2),
a(n) = (2*n+1)! [x^(2*n+1)] tan(arcsin(tan(x))),
a(n) = (2*n+1)! [x^(2*n+1)] sinh(arctanh(tan(x))).
(End)
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MAPLE
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S:= series(tan(x)/sqrt(1-tan(x)^2), x, 102):
seq(coeff(S, x, 2*j+1)*(2*j+1)!, j=0..50); # Robert Israel, May 08 2017
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MATHEMATICA
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nn = 20; Table[(CoefficientList[Series[Tan[x]/Sqrt[1 - Tan[x]^2], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 06 2015 *)
With[{nn=30}, Take[CoefficientList[Series[Tan[ArcSin[Tan[x]]], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Mar 22 2015 *)
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PROG
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(Maxima)
a(n):=sum(binomial(2*m, m)*sum(binomial(j+2*m, 2*m)*(j+2*m+1)!*2^(2*n-j-4*m)*(-1)^(n+m+j)*stirling2(2*n+1, j+2*m+1), j, 0, 2*n-2*m), m, 0, n)/((2*n+1)!); /* Vladimir Kruchinin, Jun 15 2011 */
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CROSSREFS
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Sequence in context: A012179 A012026 A012190 * A012046 A012151 A012156
Adjacent sequences: A012074 A012075 A012076 * A012078 A012079 A012080
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KEYWORD
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nonn
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AUTHOR
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Patrick Demichel (patrick.demichel(AT)hp.com)
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STATUS
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approved
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