|
Search: id:A121648
|
|
|
| A121648 |
|
a(n) is the square of the coefficient of x^n in 1/(1 - x*A(x^2)), where g.f. A(x) = Sum_{n>=0} a(n)*x^n. |
|
+0
5
|
|
| 1, 1, 1, 4, 9, 25, 64, 256, 729, 2601, 7921, 28900, 90000, 318096, 1016064, 3888784, 12694969, 46881409, 155825289, 592435600, 1987643889, 7408217041, 25153960000, 95823678916, 327811212304, 1227814692624, 4234507915264
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
a(n) = A121649(n)^2. G.f.: A(x^2) = (1 - 1/B(x) )/x, where B(x) = Sum_{n>=0} a(n)^(1/2)*x^n is the g.f. of A121649.
|
|
EXAMPLE
|
A(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 64*x^6 + 256*x^7 +...
Take the square-root of each term, a(n)^(1/2) and
let B(x) be the g.f. of the resulting sequence:
B(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 16*x^7 +...
Then 1/B(x) = 1 - x*A(x^2):
1/B(x) = 1 - x - x^3 - x^5 - 4*x^7 - 9*x^9 - 25*x^11 - 64*x^13 -...
|
|
PROGRAM
|
(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, polcoeff(x^(n-2*k)*(sum(j=0, k, a(j)*x^(2*j))+x*O(x^n))^(n-2*k), n))^2)}
(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+x+O(x^2); while(m<=n, m*=2; A=1/(1-x*sum(k=0, m-1, polcoeff(A, k)^2*x^(2*k), O(x^(2*m))))); polcoeff(A, n)^2)} /* Michael Somos Aug 18 2006 */
|
|
CROSSREFS
|
Cf. A121649; bisection of A121649: A121650, A121651.
Sequence in context: A160190 A032127 A007598 this_sequence A133022 A028400 A117678
Adjacent sequences: A121645 A121646 A121647 this_sequence A121649 A121650 A121651
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Aug 14 2006
|
|
|
Search completed in 0.002 seconds
|
