|
Search: id:A120955
|
|
|
| A120955 |
|
G.f. A(x) satisfies series_reversion(x/A(x))/x = 2*A(x) - (1+x). |
|
+0
2
|
|
| 1, 1, 1, 4, 25, 206, 2060, 23920, 314065, 4582300, 73393490, 1278859176, 24073541260, 486806278752, 10525038917720, 242318610557760, 5919811842140945, 152974724047702626, 4169576527021400852
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
The g.f. for A120956 = series_reversion(x/A(x))/x = 2*A(x) - (1+x).
|
|
FORMULA
|
a(n) = A120956(n)/2 for n>=2. G.f. A(x) satisfies: A( x*(2A(x)-1-x) ) = 1/(2A(x)-1-x). G.f. A(x) satisfies: A(x) = F(x/A(x)) and F(x) = A(x*F(x)) where F(x) = g.f. of A120956.
G.f. satisfies: A(x) = 2*A(x/A(x)) - 1 - x/A(x).
|
|
EXAMPLE
|
A(x) = 1 + x + x^2 + 4*x^3 + 25*x^4 + 206*x^5 + 2060*x^6 +...
The g.f. of A120956 is:
series_reversion(x/A(x))/x = 1 + x + 2*x^2 + 8*x^3 + 50*x^4 + 412*x^5 +...
Compare terms to see that A120956(n) = 2*a(n) for n>=2.
|
|
PROGRAM
|
(PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, t); A[ #A]=subst(Vec(serreverse(x/Ser(A)))[ #A], t, 0)); A[n+1]}
|
|
CROSSREFS
|
Cf. A120956.
Cf. A120970 (variant).
Sequence in context: A060910 A088159 A036242 this_sequence A061714 A005411 A105628
Adjacent sequences: A120952 A120953 A120954 this_sequence A120956 A120957 A120958
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 19 2006
|
|
|
Search completed in 0.002 seconds
|
