A193619 G.f. A(x) satisfies: A(x)^-2 + A(-x)^-2 = 2 and A(x)^2 - A(-x)^2 = -8*x.

1, -2, 6, 12, -122, -316, 4124, 11608, -169018, -495724, 7676596, 23075112, -371737956, -1135805144, 18808209528, 58139400112, -982459035322, -3063548374604, 52579900855620, 165071778169864, -2868211199377740, -9053503669975944

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

G.f.: ( (sqrt(1+64*x^2) + 1)*(sqrt(1+64*x^2) - 8*x)/2 )^(1/4).

G.f. A(x) = 1/G(x) where G(x) is the g.f. of A193618.

Example

G.f.: A(x) = 1 - 2*x + 6*x^2 + 12*x^3 - 122*x^4 - 316*x^5 + 4124*x^6 +...
where
A(x)^2 = 1 - 4*x + 16*x^2 - 256*x^4 + 8192*x^6 - 327680*x^8 +...
and
A(x)^-2 = 1 + 4*x - 64*x^3 + 2048*x^5 - 81920*x^7 + 3670016*x^9 +...

Prog

(PARI) {a(n)=local(Ox=x*O(x^n), A=((sqrt(1+64*x^2+Ox)+1)*(sqrt(1+64*x^2+Ox)-8*x)/2)^(1/4)); polcoeff(A, n)}
(PARI) N=40; x='x+O('x^N); Vec(sqrt((1-8*x+sqrt(1+64*x^2))/2)) \\ Seiichi Manyama, Aug 26 2020

Crossrefs

Cf. A193618.

Sequence in context: A089423 A062349 A325504 * A290406 A371042 A319481

Adjacent sequences: A193616 A193617 A193618 * A193620 A193621 A193622

Keyword

sign

Author

Paul D. Hanna, Aug 01 2011

Status

approved