A121650 A bisection of A121649; a(n) = A121649(2*n) = A121648(2*n)^(1/2).

1, 1, 3, 8, 27, 89, 300, 1008, 3563, 12483, 44583, 158600, 572548, 2057792, 7451924, 26913176, 98321435, 358017691, 1312060393, 4797471336, 17666696455, 64890598361, 239454075896, 881886659872, 3264772507980, 12061404124676

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

G.f.: A(x) = 1/(1 - x*B(x)^2), where B(x) = Sum_{n>=0} A121649(n)^2*x^n is the g.f. of A121648.

Example

A(x) = 1 + x + 3*x^2 + 8*x^3 + 27*x^4 + 89*x^5 + 300*x^6 +...
1/A(x) = 1 - x - 2*x^2 - 3*x^3 - 10*x^4 - 27*x^5 - 76*x^6 - 212*x^7 -...
1/A(x) = 1 - x*B(x)^2, where
B(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 27*x^4 + 76*x^5 + 212*x^6 +...
and B(x) is the g.f. of A121648 where all coefficients are squares:
B(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 64*x^6 + 256*x^7 +...

Prog

(PARI) {a(n)=local(B=1+x); if(n==0, 1, for(m=0, n, B=1/(1-x*sum(k=0, m, polcoeff(B, k)^2*x^(2*k))+O(x^(2*n+2)))); polcoeff(B, 2*n))}

Crossrefs

Cf. A121648, A121649, A121651.

Sequence in context: A148832 A148833 A210680 * A151462 A145967 A145792

Adjacent sequences: A121647 A121648 A121649 * A121651 A121652 A121653

Keyword

nonn

Author

Paul D. Hanna, Aug 14 2006

Status

approved