A277302 G.f. satisfies: A(x - 3*A(x)^2) = x + 2*A(x)^2.

1, 5, 80, 1900, 55490, 1848660, 67630080, 2657251005, 110560510400, 4824793769260, 219334788340040, 10334817935549420, 502814686712631520, 25184673137026274600, 1295595210394570426800, 68326193725188929358600, 3688253200687778850553800, 203524353764195058692833200, 11468618360097679305600299400, 659345494779348103800864088800, 38644445208422874351089132287200

Offset

1,2

Links

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

Formula

G.f. A(x) also satisfies:

(1) A(x) = x + 5 * A( 2*x/5 + 3*A(x)/5 )^2.

(2) A(x) = -2*x/3 + 5/3 * Series_Reversion(x - 3*A(x)^2).

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

(4) R( sqrt( x/5 - R(x)/5 ) ) = 3*x/5 + 2*R(x)/5, where R(A(x)) = x.

a(n) = Sum_{k=0..n-1} A277295(n,k) * 3^k * 5^(n-k-1).

Example

G.f.: A(x) = x + 5*x^2 + 80*x^3 + 1900*x^4 + 55490*x^5 + 1848660*x^6 + 67630080*x^7 + 2657251005*x^8 + 110560510400*x^9 + 4824793769260*x^10 +...

Prog

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

Crossrefs

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

Cf. A277300, A277301, A277303, A277304, A277305, A277306, A277307, A277308, A277309.

Cf. A276364.

Sequence in context: A269792 A144344 A062364 * A189443 A275091 A275347

Adjacent sequences: A277299 A277300 A277301 * A277303 A277304 A277305

Keyword

nonn

Author

Paul D. Hanna, Oct 09 2016

Status

approved