A212380 G.f. satisfies: A(x) = x^2 + A(A(x))/x.

1, 1, 2, 6, 19, 65, 231, 849, 3193, 12238, 47614, 187578, 746731, 2999264, 12139398, 49463204, 202729889, 835242106, 3457178366, 14369424882, 59949943825, 250967906314, 1053891879086, 4438207804725, 18739249857981, 79312365115719, 336430161046134

Offset

2,3

Links

Table of n, a(n) for n=2..28.

Formula

G.f. satisfies: A(x) = ( A(x)^3 + A(A(A(x))) ) / A(A(x)).

Example

 G.f.: A(x) = x^2 + x^3 + 2*x^4 + 6*x^5 + 19*x^6 + 65*x^7 + 231*x^8 +...
such that
A(A(x)) = x^4 + 2*x^5 + 6*x^6 + 19*x^7 + 65*x^8 + 231*x^9 +...+ a(n+1)*x^(n+2) +...
Related expansions:
A(A(A(x))) = x^8 + 4*x^9 + 16*x^10 + 62*x^11 + 243*x^12 + 956*x^13 +...
A(x)^3 = x^6 + 3*x^7 + 9*x^8 + 31*x^9 + 111*x^10 + 411*x^11 + 1556*x^12 +...
A(x)*A(A(x)) = x^6 + 3*x^7 + 10*x^8 + 35*x^9 + 127*x^10 + 473*x^11 + 1799*x^12 +...
where A(x)*A(A(x)) = A(x)^3 + A(A(A(x))).

Prog

 (PARI) {a(n)=local(A=x^2+x^3); for(i=1, n, A=x^2+subst(A, x, A+x*O(x^n))/x); polcoeff(A, n)}
for(n=2, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A047016 A307354 A307487 * A150084 A275755 A150085

Adjacent sequences: A212377 A212378 A212379 * A212381 A212382 A212383

Keyword

nonn

Author

Paul D. Hanna, May 11 2012

Status

approved