A212527 G.f. satisfies: A(x) = 1 + x*A(x)^2 / (A(I*x) * A(-I*x)).

1, 1, 2, 8, 26, 56, 194, 832, 2866, 7904, 30690, 137000, 497706, 1491512, 6041602, 27557184, 102985186, 321675648, 1333006018, 6160815624, 23426000186, 75016874488, 315357132994, 1470462300160, 5656904907026, 18419315779552, 78201118018466, 366962271138472

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 26*x^4 + 56*x^5 + 194*x^6 + 832*x^7 +...
Related expansions begin:
A(x)^2 = 1 + 2*x + 5*x^2 + 20*x^3 + 72*x^4 + 196*x^5 + 668*x^6 + 2692*x^7 +...
A(I*x)*A(-I*x) = 1 - 3*x^2 + 40*x^4 - 316*x^6 + 4624*x^8 - 50676*x^10 + 811192*x^12 -+...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A^2/(subst(A, x, I*x+x*O(x^n))*subst(A, x, -I*x+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A143339, A216681, A216712, A216713.

Sequence in context: A102942 A212691 A206803 * A227015 A216929 A100504

Adjacent sequences: A212524 A212525 A212526 * A212528 A212529 A212530

Keyword

nonn

Author

Paul D. Hanna, Jun 13 2012

Status

approved