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!)
A303924 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 1 + x*A(x)^(n+1) - A(x) )^n. 3
1, 1, 2, 5, 15, 52, 204, 891, 4266, 22092, 122358, 718282, 4438154, 28711805, 193700970, 1358588449, 9883071724, 74423630202, 579231718432, 4652864427983, 38528749877802, 328519744186940, 2881366257269722, 25969840412367362, 240307819488203558, 2280902112035109237, 22187847195528993904, 221024332987155498348 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f. A(x) satisfies:
(1) 1 = Sum_{n>=0} ( 1 + x*A(x)^(n+1) - A(x) )^n.
(2) 1 = Sum_{n>=0} x^n * A(x)^(n*(n+1)) / (1 + (A(x)-1)*A(x)^n)^(n+1). - Paul D. Hanna, Dec 11 2018
G.f.: 1/x*Series_Reversion( x/F(x) ) such that 1 = Sum_{n>=0} ((1 + x*F(x))^n - F(x))^n, where F(x) is the g.f. of A303923.
G.f.: x/Series_Reversion( x*G(x) ) such that 1 = Sum_{n>=0} ((1 + x*G(x))^(n+2) - G(x))^n, where G(x) is the g.f. of A303925.
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 52*x^5 + 204*x^6 + 891*x^7 + 4266*x^8 + 22092*x^9 + 122358*x^10 + 718282*x^11 + 4438154*x^12 + ...
such that
1 = 1 + (1 + x*A(x)^2 - A(x)) + (1 + x*A(x)^3 - A(x))^2 + (1 + x*A(x)^4 - A(x))^3 + (1 + x*A(x)^5 - A(x))^4 + (1 + x*A(x)^6 - A(x))^5 + ...
PROG
(PARI) {a(n) = my(A=[1]); for(i=0, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, ( 1 + x*Ser(A)^(m+1) - Ser(A))^m ) )[#A] ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
Sequence in context: A292935 A000110 A336022 * A336021 A186001 A134381
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 03 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 April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)