A385205 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^4 )^(1/5).

1, 5, 50, 500, 4375, 27500, 0, -3562500, -70078125, -876562500, -6926562500, 0, 1189169921875, 25690820312500, 346441406250000, 2911880859375000, 0, -550017993164062500, -12339622131347656250, -171953389892578125000, -1487552714691162109375, 0

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = 25^n * binomial(4*n/5+1/5,n)/(4*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^3).

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(4/5)) )^(1/4).

a(5*n+1) = 0 for n > 0.

G.f.: 1/B(x), where B(x) is the g.f. of A299958.

Mathematica

a[n_] := 25^n * Binomial[4*n/5 + 1/5, n]/(4*n + 1); Array[a, 22, 0] (* Amiram Eldar, Nov 25 2025 *)

Prog

(PARI) a(n) = 25^n*binomial(4*n/5+1/5, n)/(4*n+1);

Crossrefs

Cf. A078534, A299958, A385203, A385204.

Cf. A182122, A376636, A385207.

Sequence in context: A136918 A136910 A267663 * A093143 A346937 A077330

Adjacent sequences: A385202 A385203 A385204 * A385206 A385207 A385208

Keyword

sign

Author

Seiichi Manyama, Jun 21 2025

Status

approved