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!)
A317355 E.g.f. satisfies: A(x) = Sum_{n>=0} ( exp(n*x) - A(x) )^n / (2 - exp(n*x)*A(x))^(n+1). 3
1, 1, 5, 85, 5261, 549061, 79707245, 15531175045, 3926159465261, 1249497583485061, 488841071584907885, 230674363972514998405, 129251110556658394610861, 84870052450743141454787461, 64574784437643167984687238125, 56377769340759003121860283852165, 55996026841326090728124344073814061 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
E.g.f. A(x) = G(exp(x) - 1), where G(x) is the g.f. of A317350.
LINKS
FORMULA
E.g.f. A(x) satisfies:
(1) A(x) = Sum_{n>=0} ( exp(n*x) - A(x) )^n / (2 - exp(n*x)*A(x))^(n+1),
(2) A(x) = Sum_{n>=0} ( exp(n*x) + A(x) )^n / (2 + exp(n*x)*A(x))^(n+1).
a(n) ~ c * d^n * (n!)^2 / sqrt(n), where d = A317904 = 3.9561842030261697545408... and c = 0.16545672527... - Vaclav Kotesovec, Aug 10 2018
EXAMPLE
E.g.f.: A(x) = 1 + x + 5*x^2/2! + 85*x^3/3! + 5261*x^4/4! + 549061*x^5/5! + 79707245*x^6/6! + 15531175045*x^7/7! + 3926159465261*x^8/8! + 1249497583485061*x^9/9! + ...
such that A = A(x) satisfies
A(x) = 1/(2 - A) + (exp(x) - A)/(2 - exp(x)*A)^2 + (exp(2*x) - A)^2/(2 - exp(2*x)*A)^3 + (exp(3*x) - A)^3/(2 - exp(3*x)*A)^4 + (exp(4*x) - A)^4/(2 - exp(4*x)*A)^5 + (exp(5*x) - A)^5/(2 - exp(5*x)*A)^6 + ...
Also,
A(x) = 1/(2 + A) + (exp(x) + A)/(2 + exp(x)*A)^2 + (exp(2*x) + A)^2/(2 + exp(2*x)*A)^3 + (exp(3*x) + A)^3/(2 + exp(3*x)*A)^4 + (exp(4*x) + A)^4/(2 + exp(4*x)*A)^5 + (exp(5*x) + A)^5/(2 + exp(5*x)*A)^6 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A = Vec( sum(m=0, #A, ( exp(m*x +x*O(x^#A)) - Ser(A) )^m / (2 - exp(m*x +x*O(x^#A))*Ser(A))^(m+1) ) ) ); n!*A[n+1]}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A192055 A012815 A113107 * A018925 A309327 A363424
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 02 2018
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 February 22 18:10 EST 2024. Contains 370260 sequences. (Running on oeis4.)