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A200560 E.g.f.: arcsin(x) o x/(1-x) o sin(x), a composition of functions involving sin(x) and its inverse. 3
1, 2, 6, 28, 180, 1502, 15456, 189208, 2683920, 43263962, 780807456, 15593180788, 341340941760, 8126644655222, 209050212857856, 5777935570510768, 170755837008595200, 5373097909706399282, 179351443518333574656, 6329687401322560131148, 235491796312126982538240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Given e.g.f. A(x), then A(Pi/6) = Pi/2, where Pi/6 is the radius of convergence.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..250

FORMULA

E.g.f. A(x) satisfies: A(-A(-x)) = x.

The n-th iteration of e.g.f. A(x) equals: arcsin(x) o x/(1-n*x) o sin(x) = arcsin( sin(x)/(1-n*sin(x)) ).

a(n) ~ 2^n * 3^(n-1/4) * n^(n-1) / (Pi^(n-1/2) * exp(n)). - Vaclav Kotesovec, Apr 05 2016

EXAMPLE

E.g.f.: A(x) = x + 2*x^2/2! + 6*x^3/3! + 28*x^4/4! + 180*x^5/5! +...

where the initial iterations of e.g.f. A(x) begin:

A(A(x)) = arcsin( sin(x)/(1-2*sin(x)) ); more explicitly,

A(A(x)) = x + 4*x^2/2! + 24*x^3/3! + 200*x^4/4! + 2160*x^5/5! +...

A(A(A(x))) = arcsin( sin(x)/(1-3*sin(x)) ); more explicitly,

A(A(A(x))) = x + 6*x^2/2! + 54*x^3/3! + 660*x^4/4! + 10260*x^5/5! +...

A(A(A(A(x)))) = arcsin( sin(x)/(1-4*sin(x)) ); more explicitly,

A(A(A(A(x)))) = x + 8*x^2/2! + 96*x^3/3! + 1552*x^4/4! + 31680*x^5/5! +...

PROG

(PARI) {a(n)=n!*polcoeff(subst(asin(x+x*O(x^n)), x, subst(x/(1-x), x, sin(x+x*O(x^n)))), n)}

CROSSREFS

Sequence in context: A276911 A104018 A100526 * A303344 A355205 A196555

Adjacent sequences:  A200557 A200558 A200559 * A200561 A200562 A200563

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 29 2011

STATUS

approved

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Last modified August 14 23:38 EDT 2022. Contains 356122 sequences. (Running on oeis4.)