The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A352815 G.f. A(x) satisfies: 1 + x = Sum_{n>=0} (-1)^n * (x^n + A(x))^(n+1). 1
1, 4, 15, 62, 263, 1153, 5187, 23792, 110898, 523773, 2501268, 12057407, 58593831, 286743949, 1411905287, 6989973590, 34773216944, 173737947911, 871442154413, 4386482848975, 22150822685669, 112185906664804, 569713055956736, 2900350345874632, 14799219791196091 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f. A(x) satisfies:
(1) 1 + x = Sum_{n>=0} (-1)^n * (x^n + A(x))^(n+1).
(2) -x = Sum_{n>=0} (-1)^n * x^(n*(n-1)) / (1 + x^n*A(x))^(n+1).
EXAMPLE
G.f.: A(x) = x + 4*x^2 + 15*x^3 + 62*x^4 + 263*x^5 + 1153*x^6 + 5187*x^7 + 23792*x^8 + 110898*x^9 + 523773*x^10 + ...
where
1 + x = (1 + A(x)) - (x + A(x))^2 + (x^2 + A(x))^3 - (x^3 + A(x))^4 + (x^4 + A(x))^5 - (x^5 + A(x))^6 + (x^6 + A(x))^7 + ...
also
-x = 1/(1 + A(x)) - 1/(1 + x*A(x))^2 + x^2/(1 + x^2*A(x))^3 - x^6/(1 + x^3*A(x))^4 + x^12/(1 + x^4*A(x))^5 - x^20/(1 + x^5*A(x))^6 + ...
Specific values.
A(x) = 1 at x = 0.1834970136530040531685106821803389905413247357336272...
PROG
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = -polcoeff( sum(m=0, #A, (-1)^m*(x^m + x*Ser(A))^(m+1) ), #A)); A[n]}
for(n=1, 40, print1(a(n), ", "))
(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=0, sqrtint(#A)+1, (-1)^m*x^(m*(m-1))/(1 + x^m*x*Ser(A))^(m+1) ), #A)); A[n]}
for(n=1, 40, print1(a(n), ", "))
CROSSREFS
Cf. A317997.
Sequence in context: A151484 A275871 A007161 * A007167 A036728 A027216
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 04 2022
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 May 26 15:04 EDT 2024. Contains 372826 sequences. (Running on oeis4.)