A276366 G.f. A(x) satisfies: A(x - A(x)^3) = x + A(x)^2.

1, 1, 3, 12, 57, 300, 1697, 10126, 62991, 405247, 2680901, 18160444, 125562250, 883868590, 6321838520, 45869309028, 337167193262, 2508018933431, 18861358215299, 143293615189089, 1098997404472941, 8504070741463729, 66358269984208701, 521923129718567918, 4136089275165532156, 33013640650845937124

Offset: 1

Author

Paul D. Hanna, Sep 01 2016

Keywords

• nonn

Examples

			G.f.: A(x) = x + x^2 + 3*x^3 + 12*x^4 + 57*x^5 + 300*x^6 + 1697*x^7 + 10126*x^8 + 62991*x^9 + 405247*x^10 + 2680901*x^11 + 18160444*x^12 +...
such that A(x - A(x)^3) = x + A(x)^2.
RELATED SERIES.
A(x - A(x)^3) = x + x^2 + 2*x^3 + 7*x^4 + 30*x^5 + 147*x^6 + 786*x^7 + 4480*x^8 + 26814*x^9 + 166865*x^10 + 1072160*x^11 + 7076724*x^12 +...
which equals x + A(x)^2.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A153851, A275765, A276364.

Programs

PARI

{a(n) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -polcoeff(subst(F, x, x-F^3) - F^2, #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Formula

G.f. A(x) satisfies: A'(x - A(x)^3) = (1 + 2*A'(x)*A(x)) / (1 - 3*A'(x)*A(x)^2).