A277305 G.f. satisfies: A(x - 5*A(x)^2) = x + A(x)^2.

1, 6, 132, 4350, 176964, 8235252, 421814232, 23252672574, 1359954622860, 83572511671092, 5359130778285096, 356786692299782916, 24565803644793789192, 1744056102774572824920, 127369971591949093219920, 9550397045409732902387790, 734084078724419876468356500, 57766855968717521513179054860, 4648888743682938087701732224680

Offset: 1

Author

Paul D. Hanna, Oct 09 2016

Keywords

• nonn

Examples

			G.f.: A(x) = x + 6*x^2 + 132*x^3 + 4350*x^4 + 176964*x^5 + 8235252*x^6 + 421814232*x^7 + 23252672574*x^8 + 1359954622860*x^9 + 83572511671092*x^10 +...
		

Links

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

Crossrefs

Cf. A277295, A213591, A275765, A276360, A276361, A276362, A276363.

Cf. A277300, A277301, A277302, A277303, A277304, A277306, A277307, A277308, A277309.

Cf. 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 - 5*F^2) - F^2, #A) ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Formula

G.f. A(x) also satisfies:

(1) A(x) = x + 6 * A( x/6 + 5*A(x)/6 )^2.

(2) A(x) = -x/5 + 6/5 * Series_Reversion(x - 5*A(x)^2).

(3) R(x) = -5*x + 6 * Series_Reversion(x + A(x)^2), where R(A(x)) = x.

(4) R( sqrt( x/6 - R(x)/6 ) ) = 5*x/6 + R(x)/6, where R(A(x)) = x.

a(n) = Sum_{k=0..n-1} A277295(n,k) * 5^k * 6^(n-k-1).