A213010 G.f. satisfies: A(x) = x+x^2 + x*A(A(x)).

1, 2, 4, 16, 80, 480, 3296, 25152, 209600, 1884160, 18110080, 184898304, 1994964736, 22654449664, 269855506944, 3362350046208, 43715434232832, 591812683833344, 8326660788725760, 121550217508892672, 1838089917983911936, 28753297176215257088, 464675647688625364992

Offset

1,2

Comments

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

Links

Paul D. Hanna, Table of n, a(n) for n = 1..256

Formula

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

Example

G.f.: A(x) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...
where
A(A(x)) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...
Related expansions.
Let B(B(x)) = A(x), then B(x) is an integer series:
B(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 + 6133*x^8 +...
where the coefficients of B(x) are congruent to 1 modulo 4.

Prog

(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)}
for(n=1, 31, print1(a(n), ", "))

Crossrefs

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

Sequence in context: A025225 A115125 A326859 * A000831 A000090 A295922

Adjacent sequences: A213007 A213008 A213009 * A213011 A213012 A213013

Keyword

nonn

Author

Paul D. Hanna, Jun 01 2012

Status

approved