A193234 G.f.: A(x) = ( 1 + Sum_{n>=1} 2*(-2)^n * x^(n^2) )^(-1/2).

1, 2, 6, 20, 66, 228, 804, 2872, 10374, 37780, 138436, 509832, 1885396, 6996472, 26039592, 97160592, 363332534, 1361320284, 5109306148, 19205627608, 72292274076, 272454449560, 1027979651384, 3882579544656, 14677889406396, 55536827825096

Offset

0,2

Comments

Compare the g.f. to the theta_3 series: 1 + Sum_{n>=1} 2*x^(n^2).

Links

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

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 66*x^4 + 228*x^5 + 804*x^6 +...
where
1/A(x)^2 = 1 - 4*x + 8*x^4 - 16*x^9 + 32*x^16 - 64*x^25 + 128*x^36 - 256*x^49 + 512*x^64 +...+ 2*(-2)^n*x^(n^2) +...

Prog

(PARI) {a(n)=local(S=1+sum(m=1, sqrtint(n), 2*(-2)^m*x^(m^2))+x*O(x^n)); polcoeff(S^(-1/2), n)}

Crossrefs

Cf. A193235.

Sequence in context: A246019 A226510 A108627 * A285197 A372872 A148475

Adjacent sequences: A193231 A193232 A193233 * A193235 A193236 A193237

Keyword

nonn

Author

Paul D. Hanna, Jul 18 2011

Status

approved