A143049 G.f. satisfies A(x) = 1 + x*A(-x)^6.

1, 1, -6, -21, 286, 1281, -20592, -100226, 1749462, 8899086, -162993402, -852079872, 16106878320, 85783258295, -1658113447608, -8950840125828, 175904428301062, 959332126312266, -19096256882857668, -104984591307499239, 2111233112316364434

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Formula

G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^6)^6.

G.f. satisfies: [A(x)^7 + A(-x)^7]/2 = [A(x)^6 + A(-x)^6]/2.

Example

A(x) = 1 + x - 6*x^2 - 21*x^3 + 286*x^4 + 1281*x^5 - 20592*x^6 -++-...
A(x)^6 = 1 + 6*x - 21*x^2 - 286*x^3 + 1281*x^4 + 20592*x^5 - 100226*x^6 -...
A(x)^7 = 1 + 7*x - 21*x^2 - 364*x^3 + 1281*x^4 + 27027*x^5 - 100226*x^6 -...
Note that a bisection of A^7 equals a bisection of A^6.

Prog

(PARI) a(n)=local(A=x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, -x)^6); polcoeff(A, n)

Crossrefs

Cf. A143045, A143046, A143047, A143048, A213252, A213281, A213335.

Cf. A171206.

Sequence in context: A131960 A372137 A244299 * A213680 A164643 A190275

Adjacent sequences: A143046 A143047 A143048 * A143050 A143051 A143052

Keyword

sign

Author

Paul D. Hanna, Jul 19 2008

Status

approved