A193378 Imaginary part of g.f. C(x) that satisfies: C(x) = 1 + x*C(I*x)^2.

2, -4, 2, -4, -20, 56, -126, -4, 308, -696, 5444, 7224, -7272, -14224, -191022, -450404, 39524, 2309416, 5059084, 20045736, 18158632, -170205936, -18475212, -725028200, -1746739960, 9540210896, -10852826168, 16441084912, 107790254896, -422324078368, 1055213939634

Offset

2,1

Links

Table of n, a(n) for n=2..32.

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); imag(polcoeff(A, n))}

Crossrefs

Cf. A193377 (real), A193379 (norm).

Sequence in context: A198285 A136620 A139548 * A108445 A263424 A279527

Adjacent sequences: A193375 A193376 A193377 * A193379 A193380 A193381

Keyword

sign

Author

Paul D. Hanna, Jul 24 2011

Status

approved