A143048 G.f. satisfies A(x) = 1 + x*A(-x)^5.

1, 1, -5, -15, 165, 630, -8151, -33780, 474045, 2052495, -30206330, -134392230, 2040588775, 9248893360, -143569282680, -659546365020, 10407737293965, 48303692377425, -771991701692175, -3611789245335285, 58311219888996170, 274581478640096340

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)^5)^5.

G.f. satisfies: [A(x)^6 + A(-x)^6]/2 = [A(x)^5 + A(-x)^5]/2.

Example

A(x) = 1 + x - 5*x^2 - 15*x^3 + 165*x^4 + 630*x^5 - 8151*x^6 -++-...
A(x)^5 = 1 + 5*x - 15*x^2 - 165*x^3 + 630*x^4 + 8151*x^5 - 33780*x^6 -...
A(x)^6 = 1 + 6*x - 15*x^2 - 220*x^3 + 630*x^4 + 11286*x^5 - 33780*x^6 -...
Note that a bisection of A^6 equals a bisection of A^5.

Prog

(PARI) a(n)=local(A=x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, -x)^5); polcoeff(A, n)

Crossrefs

Cf. A143045, A143046, A143047, A143049, A213252, A213281, A213335.

Cf. A171204.

Sequence in context: A048347 A034980 A174850 * A261843 A120602 A004130

Adjacent sequences: A143045 A143046 A143047 * A143049 A143050 A143051

Keyword

sign

Author

Paul D. Hanna, Jul 19 2008

Status

approved