A191565 G.f. satisfies: A(A(x))^2 = A(x)^2 + 4*x^3.

1, 2, -14, 184, -3194, 65472, -1503924, 37593664, -1004163802, 28314667072, -835650200380, 25652840146624, -815280469973380, 26728163562423360, -901336722528156712, 31194183364269262848, -1105930698812430437626

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

G.f.: A(x) = x + 2*x^2 - 14*x^3 + 184*x^4 - 3194*x^5 + 65472*x^6 +...
Illustrate A(A(x))^2 - A(x)^2 = 4*x^3 with the expansions:
A(x)^2 = x^2 + 4*x^3 - 24*x^4 + 312*x^5 - 5456*x^6 + 113016*x^7 +...
A(A(x))^2 = x^2 + 8*x^3 - 24*x^4 + 312*x^5 - 5456*x^6 + 113016*x^7 +...
A(A(x)) = x + 4*x^2 - 20*x^3 + 236*x^4 - 3872*x^5 + 76716*x^6 - 1723488*x^7 +...
Let R(x) be the series reversion of A(x):
R(x) = x - 2*x^2 + 22*x^3 - 364*x^4 + 7390*x^5 - 170556*x^6 +...
R(x)^3 = x^3 - 6*x^4 + 78*x^5 - 1364*x^6 + 28254*x^7 - 655668*x^8 +...
where A(x)^2 = x^2 + 4*R(x)^3.

Prog

(PARI) {a(n)=local(A=x+x^2+x*O(x^n)); for(i=1, n, A=A-(subst(A, x, A)-x*sqrt(4*x+A^2/x^2))); polcoeff(A, n)}

Crossrefs

Cf. A191557, 107700, A138740.

Sequence in context: A258872 A372246 A000807 * A191236 A217905 A370940

Adjacent sequences: A191562 A191563 A191564 * A191566 A191567 A191568

Keyword

sign

Author

Paul D. Hanna, Jun 06 2011

Status

approved