|
Search: id:A143135
|
|
|
| A143135 |
|
E.g.f. satisfies: A(x) = sin(x + A(x)^2) with A(0)=0. |
|
+0
3
|
|
| 1, 2, 11, 100, 1261, 20342, 399671, 9256840, 246907321, 7452534122, 251099460611, 9341422237420, 380293239870181, 16815919738248542, 802553031266952431, 41117164304824602640, 2250747364089063475441
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Radius of convergence of A(x) is r = Pi/4 - 1/2, with A(r) = sqrt(2)/2.
|
|
FORMULA
|
E.g.f.: A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134.
E.g.f. derivative: A'(x) = sqrt(1 - A(x)^2)/(1 - 2*A(x)*sqrt(1 - A(x)^2)).
|
|
EXAMPLE
|
A(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1261*x^5/5! +...
A(x) = sin(G(x)) where G(x) = x + A(x)^2 is the e.g.f. of A143134:
G(x) = x + 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
|
|
PROGRAM
|
(PARI) {a(n)=local(A=x); for(i=0, n, A=x + sin(A)^2); n!*polcoeff(sin(A), n)}
(PARI) {a(n)=n!*polcoeff(sin(serreverse(x-sin(x+x*O(x^n))^2)), n)}
|
|
CROSSREFS
|
Cf. A143134, A143137.
Sequence in context: A020559 A003579 A099169 this_sequence A056732 A157715 A001271
Adjacent sequences: A143132 A143133 A143134 this_sequence A143136 A143137 A143138
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008
|
|
|
Search completed in 0.002 seconds
|
