A213628 G.f. satisfies: A(x) = 1 - (x^2/A(x)) / A( x^2/A(x) ).

1, 1, 3, 14, 85, 616, 5072, 46013, 450739, 4702265, 51731956, 595874703, 7147366614, 88905147730, 1143097097833, 15152617826426, 206646826047563, 2894398418226395, 41577147999077079, 611779190051375147, 9211548488261257610, 141802624561414800815

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Formula

G.f.: A(x) = x^2/(x - G(x)^2) where G(x) is the g.f. of A213591 such that G(x^2/A(x)) = G(x - G(x)^2) = x.

G.f.: A(x) = Series_Reversion(x*F(x)) where F(x) = 1 + x*F(1 - 1/F(x))^2 is the g.f. of A212411.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 85*x^5 + 616*x^6 + 5072*x^7 +...
Related expansions:
x^2/A(x) = x - x^2 - 2*x^3 - 9*x^4 - 56*x^5 - 420*x^6 - 3572*x^7 -...
A(x^2/A(x)) = x - x^3 - 7*x^4 - 50*x^5 - 395*x^6 - 3436*x^7 -...
A(x) = x^2/Series_Reversion(G(x)) where G(x) is the g.f. of A213591:
G(x) = x + x^2 + 4*x^3 + 24*x^4 + 178*x^5 + 1512*x^6 + 14152*x^7 +...
such that G(x - G(x)^2) = x.

Prog

(PARI) {a(n)=local(A=x, G=x); if(n<1, 0, for(i=1, n, G=serreverse(x - G^2+x*O(x^n))); A=x^2/(x-G^2); polcoeff(A, n))}
for(n=1, 25, print1(a(n), ", "))

Crossrefs

Cf. A213591, A212411.

Sequence in context: A301934 A160881 A263187 * A088716 A005189 A331608

Adjacent sequences: A213625 A213626 A213627 * A213629 A213630 A213631

Keyword

nonn

Author

Paul D. Hanna, Jun 16 2012

Status

approved