|
Search: id:A120590
|
|
|
| A120590 |
|
G.f. satisfies: 4*A(x) = 3 + x + A(x)^3, starting with [1,1,3]. |
|
+0
4
|
|
| 1, 1, 3, 19, 150, 1326, 12558, 124590, 1278189, 13449205, 144342627, 1573990275, 17389407984, 194228357568, 2189610888840, 24881753664840, 284708154606318, 3277578288381318, 37934510719585350, 441152315040444150
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
See comments in A120588 for conditions needed for an integer sequence to satisfy a functional equation of the form: r*A(x) = c + b*x + A(x)^n.
|
|
FORMULA
|
G.f.: A(x) = 1 + Series_Reversion(1+4*x - (1+x)^3). Lagrange Inversion yields: G.f.: A(x) = Sum_{n>=0} C(3*n,n)/(2*n+1)*(3+x)^(2*n+1)/4^(3*n+1).
|
|
EXAMPLE
|
A(x) = 1 + x + 3*x^2 + 19*x^3 + 150*x^4 + 1326*x^5 + 12558*x^6 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 76*x^3 + 600*x^4 + 5304*x^5 + 50232*x^6 +...
|
|
PROGRAM
|
(PARI) {a(n)=local(A=1+x+3*x^2+x*O(x^n)); for(i=0, n, A=A-4*A+3+x+A^3); polcoeff(A, n)}
|
|
CROSSREFS
|
Cf. A120591 (A(x)^3); A120588, A120592 - A120607.
Sequence in context: A074546 A054316 A006289 this_sequence A007112 A007111 A113013
Adjacent sequences: A120587 A120588 A120589 this_sequence A120591 A120592 A120593
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 16 2006, Jan 24 2008
|
|
|
Search completed in 0.002 seconds
|
