|
Search: id:A143739
|
|
|
| A143739 |
|
G.f. A(x) satisfies: A(x) = (1-x)^3*A(x)^2 - x^2*A'(x). |
|
+0
1
|
|
| 1, 3, 9, 28, 90, 300, 1051, 3975, 16971, 86584, 550560, 4354308, 41245021, 448722207, 5443128597, 72294557416, 1039558994214, 16059538853232, 264996063891607, 4648786414414347, 86363450200625247, 1693336666564186012
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 + 3*x + 9*x^2 + 28*x^3 + 90*x^4 + 300*x^5 + 1051*x^6 +...
A(x)^2 = 1 + 6*x + 27*x^2 + 110*x^3 + 429*x^4 + 1644*x^5 + 6306*x^6 +...
(1-x)^3*A(x)^2 = 1 + 3*x + 12*x^2 + 46*x^3 + 174*x^4 + 660*x^5 +...
x^2*A'(x) = 3*x^2 + 18*x^3 + 84*x^4 + 360*x^5 + 1500*x^6 + 6306*x^7 +...
|
|
PROGRAM
|
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=(1+x^2*deriv(A)/A)/(1-x)^3); polcoeff(A, n)}
|
|
CROSSREFS
|
Cf. A137553 (variant).
Sequence in context: A033190 A071724 A000245 this_sequence A047047 A071744 A071748
Adjacent sequences: A143736 A143737 A143738 this_sequence A143740 A143741 A143742
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Sep 05 2008
|
|
|
Search completed in 0.002 seconds
|
