A213010 - OEIS

%I #11 Aug 03 2012 14:52:45

%S 1,2,4,16,80,480,3296,25152,209600,1884160,18110080,184898304,

%T 1994964736,22654449664,269855506944,3362350046208,43715434232832,

%U 591812683833344,8326660788725760,121550217508892672,1838089917983911936,28753297176215257088,464675647688625364992

%N G.f. satisfies: A(x) = x+x^2 + x*A(A(x)).

%C The half-iteration of the g.f. equals an integer series (A213009).

%H Paul D. Hanna, <a href="/A213010/b213010.txt">Table of n, a(n) for n = 1..256</a>

%F G.f. satisfies: A(x) = x/G(x) - 1 - G(x) where A(G(x)) = x.

%e G.f.: A(x) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...

%e where

%e A(A(x)) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...

%e Related expansions.

%e Let B(B(x)) = A(x), then B(x) is an integer series:

%e B(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 + 6133*x^8 +...

%e where the coefficients of B(x) are congruent to 1 modulo 4.

%o (PARI) {a(n)=local(A=x+2*x^2);for(i=1,n,A=x+x^2+x*subst(A,x,A+x*O(x^n)));polcoeff(A,n)}

%o for(n=1,31,print1(a(n),", "))

%Y Cf. A213009, A030266, A215114, A215116, A215118.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 01 2012