A214769 G.f. satisfies: A(x) = 1/A(-x*A(x)^9).

1, 2, 20, 220, 2280, 25920, 443744, 10057408, 215047552, 3841564160, 57161584256, 757459114112, 10427052678656, 166827795710208, 2728593278189568, 38108069305433088, 521570277192555520, 14195894062729323520, 594582326909611536384, 21399757674339677249536

Offset

0,2

Comments

Compare g.f. to: G(x) = 1/G(-x*G(x)^7) when G(x) = 1 + x*G(x)^5 (A002294).

An infinite number of functions G(x) satisfy (*) G(x) = 1/G(-x*G(x)^9); for example, (*) is satisfied by G(x) = F(m*x) = 1 + m*x*F(m*x)^5 for all m, where F(x) is the g.f. of A002294.

Links

Table of n, a(n) for n=0..19.

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)^9))/2 starting at G_0(x) = 1+2*x.

Example

G.f.: A(x) = 1 + 2*x + 20*x^2 + 220*x^3 + 2280*x^4 + 25920*x^5 + 443744*x^6 +...
A(x)^5 = 1 + 10*x + 140*x^2 + 1980*x^3 + 26680*x^4 + 362432*x^5 + 5617920*x^6 +...
A(x)^9 = 1 + 18*x + 324*x^2 + 5532*x^3 + 88776*x^4 + 1386432*x^5 + 22460832*x^6 +...

Prog

(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, -x*A^9+x*O(x^n)))/2); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Crossrefs

Cf. A214761, A214762, A214763, A214764, A214765, A214766, A214767, A214768.

Sequence in context: A308945 A356853 A199761 * A227337 A127110 A361964

Adjacent sequences: A214766 A214767 A214768 * A214770 A214771 A214772

Keyword

nonn

Author

Paul D. Hanna, Jul 29 2012

Status

approved