A292810 G.f. A(x) satisfies: A( 2*x - A(x) - x^2 ) = 2*x - A(x).

1, 1, 4, 28, 264, 2992, 38496, 544464, 8298080, 134500672, 2297361024, 41077857152, 765073498368, 14786330691072, 295652808207360, 6101427222041856, 129707991377671680, 2835915576534111232, 63683889838128080896, 1467174199736163264512, 34643692576697214742528, 837694231078769706999808, 20727017363846896783998976

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Formula

G.f.: x + G(x)^2 where x = G(x) - G(x)^2 - G(G(x))^2, and G(x) is the g.f. of A177409.

Example

G.f.: A(x) = x + x^2 + 4*x^3 + 28*x^4 + 264*x^5 + 2992*x^6 + 38496*x^7 + 544464*x^8 + 8298080*x^9 + 134500672*x^10 + 2297361024*x^11 + 41077857152*x^12 + 765073498368*x^13 + 14786330691072*x^14 + 295652808207360*x^15 +...
such that A( 2*x - A(x) - x^2 ) = 2*x - A(x).

Prog

(PARI) {a(n) = my(A=x, V=[1, 1]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(G=A, x, 2*x - x^2 - A) )[#V]/(-1) ); V[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A177409.

Sequence in context: A360775 A196523 A260775 * A368892 A360727 A353013

Adjacent sequences: A292807 A292808 A292809 * A292811 A292812 A292813

Keyword

nonn

Author

Paul D. Hanna, Sep 24 2017

Status

approved