login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307999 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (1 - (-1)^n*A(x))^(n+1), where A(0) = 0. 0
1, 3, 5, 15, 65, 255, 961, 3759, 15233, 62655, 260097, 1090623, 4616769, 19698687, 84611841, 365570559, 1587755777, 6928284927, 30358910977, 133532161023, 589348292609, 2609230704639, 11584885657601, 51571340750847, 230129898799105, 1029215591587839, 4612514610282497, 20711143725961215, 93164104646180865, 419778524769746943, 1894404146662522881, 8561776644482695167 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f. A = A(x) satisfies
(1) 1 = (1 - A)/(1 - x^2*(1 - A)^2) + x*(1 + A)^2/(1 - x^2*(1 + A)^2).
(2) A = (1 + A)^2*x + ((1 + A)^3 - 4*A)*x^2 - (1 - A^2)^2*x^3 - (1 - A^2)^2*x^4.
(3) 0 = x^3*(1+x)*A^4 - x^2*A^3 - (2*x^4 + 2*x^3 + 3*x^2 + x)*A^2 + (1-x)^2*A - x*(1-x)*(1+x)^2.
EXAMPLE
G.f.: A(x) = x + 3*x^2 + 5*x^3 + 15*x^4 + 65*x^5 + 255*x^6 + 961*x^7 + 3759*x^8 + 15233*x^9 + 62655*x^10 + 260097*x^11 + 1090623*x^12 + ...
such that
1 = (1 - A(x)) + x*(1 + A(x))^2 + x^2*(1 - A(x))^3 + x^3*(1 + A(x))^4 + x^4*(1 - A(x))^5 + x^5*(1 + A(x))^6 + x^6*(1 - A(x))^7 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = polcoeff( sum(m=0, #A, x^m * (1 - (-1)^m*x*Ser(A))^(m+1) ), #A) ); A[n]}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
Sequence in context: A018719 A154107 A305873 * A018771 A214534 A270548
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 09 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 00:22 EDT 2024. Contains 371850 sequences. (Running on oeis4.)