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A121648
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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.
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4
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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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.
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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 -...
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PROG
| (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 */
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CROSSREFS
| Cf. A121649; bisection of A121649: A121650, A121651.
Sequence in context: A181357 A175627 A007598 * A133022 A184326 A176497
Adjacent sequences: A121645 A121646 A121647 * A121649 A121650 A121651
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 14 2006
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