A199917 Numerators of A(x) where A(x) satisfies A(A(x)) = (2-2*cos(x))/x.

0, 1, 0, -1, 0, -7, 0, -23, 0, -5947, 0, -140759, 0, -8265391, 0, 133286519, 0, 1088222737541, 0, 4970981405216383, 0, 7294918534710727, 0, -32299178524632916333, 0, -944164720798082858723567, 0, 2252653730296347607326319, 0, 1968938229271096381309083587

Offset

0,6

Links

Table of n, a(n) for n=0..29.

Dmitry Kruchinin, Vladimir Kruchinin, Method for solving an iterative functional equation $A^{2^n}(x)=F(x)$, arXiv:1302.1986

Formula

a(n) = numerator(T(n,1)); T(n,m) = if n=m then 1 else 1/2*(((-1)^m*2^m*((-1)^(n+m)+1)*sum(j=1..m, ((sum(i=0..(j-1)/2,(j-2*i)^(n+m) *C(j,i))) *C(m,j) *(-1)^((n+m)/2+m-j))/2^j))/(n+m)! -sum(i=m+1..n-1, T(n,i) *T(i,m))).

Example

x - 1/24*x^3 - 7/5760*x^5 - 23/193536*x^7 - 5947/464486400*x^9 + ...

Crossrefs

Sequence in context: A340952 A282071 A064854 * A279991 A282489 A281672

Adjacent sequences: A199914 A199915 A199916 * A199918 A199919 A199920

Keyword

sign

Author

Vladimir Kruchinin, Nov 12 2011

Status

approved