A214767 G.f. satisfies: A(x) = 1/A(-x*A(x)^7).

1, 2, 16, 144, 1280, 12416, 156288, 2445952, 39005696, 569584128, 7551139840, 94905663488, 1200235880448, 15657039026176, 204235121909760, 2589347043356672, 34080849916796928, 554466780012625920, 11679936697324273664, 269604415927633805312, 6025264829519275556864

Offset

0,2

Comments

Compare g.f. to: G(x) = 1/G(-x*G(x)^7) when G(x) = 1 + x*G(x)^4 (A002293).

An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^7); for example, (*) is satisfied by G(x) = F(m*x) = 1 + m*x*F(m*x)^4 for all m, where F(x) is the g.f. of A002293.

Links

Table of n, a(n) for n=0..20.

Formula

The g.f. of this sequence is the limit of the recurrence:

(*) G_{n+1}(x) = (G_n(x) + 1/G_n(-x*G_n(x)^7))/2 starting at G_0(x) = 1+2*x.

Example

 G.f.: A(x) = 1 + 2*x + 16*x^2 + 144*x^3 + 1280*x^4 + 12416*x^5 + 156288*x^6 +...
A(x)^4 = 1 + 8*x + 88*x^2 + 992*x^3 + 10896*x^4 + 121600*x^5 + 1492480*x^6 +...
A(x)^7 = 1 + 14*x + 196*x^2 + 2632*x^3 + 33712*x^4 + 424032*x^5 + 5484864*x^6 +...

Prog

 (PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^7+x*O(x^n)))/2); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A214761, A214762, A214763, A214764, A214765, A214766, A214768, A214769.

Sequence in context: A365526 A199565 A003768 * A300412 A333727 A024915

Adjacent sequences: A214764 A214765 A214766 * A214768 A214769 A214770

Keyword

nonn

Author

Paul D. Hanna, Jul 29 2012

Status

approved