A303653 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 3*(1+x)^n - A(x) )^n / 3^(n+1).

1, 15, 291, 20868, 2501535, 406641390, 82021892979, 19576367780568, 5370958558206975, 1661471768423203359, 571522497313691705223, 216322544080204799422227, 89344723486622904627485286, 39989870323587920736747152457, 19285197574525200774860259575856, 9970552400727667627167081347333058, 5502200681071110455003310691040648913

Offset: 0

Author

Paul D. Hanna, Apr 28 2018

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 15*x + 291*x^2 + 20868*x^3 + 2501535*x^4 + 406641390*x^5 + 82021892979*x^6 + 19576367780568*x^7 + 5370958558206975*x^8 + ...
such that
1 = 1/3  +  (3*(1+x) - A(x))/3^2  +  (3*(1+x)^2 - A(x))^2/3^3  +  (3*(1+x)^3 - A(x))^3/3^4  +  (3*(1+x)^4 - A(x))^4/3^5  +  (3*(1+x)^5 - A(x))^5/3^6 + ...
Also,
1 = 1/(3 + A(x))  +  3*(1+x)/(3 + (1+x)*A(x))^2  +  3^2*(1+x)^4/(3 + (1+x)^2*A(x))^3  +  3^3*(1+x)^9/(3 + (1+x)^3*A(x))^4  +  3^4*(1+x)^16/(3 + (1+x)^4*A(x))^5  +  3^5*(1+x)^25/(3 + (1+x)^5*A(x))^6  + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A301436.

Formula

G.f.: 1 = Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n * A(x))^(n+1).