A193379 Norm of coefficients in g.f. C(x) that satisfies: C(x) = 1 + x*C(I*x)^2.

1, 1, 4, 17, 20, 212, 464, 4361, 17812, 60532, 123088, 4117252, 29724752, 84585040, 430795584, 8219554697, 47479991380, 214977407060, 898098431312, 16268050731620, 98128441675472, 417822285118032, 1654860158000960, 35730391312348996, 243329575991962320

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Example

G.f.: C(x) = 1 + x + 2*I*x^2 + (-1 - 4*I)*x^3 + (-4 + 2*I)*x^4 + (-14 - 4*I)*x^5 + (8 - 20*I)*x^6 + (35 + 56*I)*x^7 + (44 - 126*I)*x^8 + (246 - 4*I)*x^9 + (168 + 308*I)*x^10 +...
where
C(x)^2 = 1 + 2*x + (1 + 4*I)*x^2 + (-2 - 4*I)*x^3 + (-14 - 4*I)*x^4 + (-20 - 8*I)*x^5 + (-35 - 56*I)*x^6 + (126 + 44*I)*x^7 + (246 - 4*I)*x^8 +...
The real part of the g.f. begins:
real(C(x)) = 1 + x - x^3 - 4*x^4 - 14*x^5 + 8*x^6 + 35*x^7 + 44*x^8 + 246*x^9 + 168*x^10 - 1906*x^11 + 296*x^12 +...
The imaginary part of the g.f. begins:
imag(C(x)) = 2*x^2 - 4*x^3 + 2*x^4 - 4*x^5 - 20*x^6 + 56*x^7 - 126*x^8 - 4*x^9 + 308*x^10 - 696*x^11 + 5444*x^12 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*subst(A, x, I*x +x*O(x^n))^2); norm(polcoeff(A, n))}

Crossrefs

Cf. A193377 (real), A193378 (imag).

Sequence in context: A128981 A212748 A032828 * A022134 A041529 A042033

Adjacent sequences: A193376 A193377 A193378 * A193380 A193381 A193382

Keyword

nonn

Author

Paul D. Hanna, Jul 24 2011

Status

approved