A380466 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^3 )^(1/5).

1, 5, 150, 6250, 301875, 15868125, 881237500, 50865750000, 3021240234375, 183454158593750, 11336659803906250, 710625236343750000, 45075347315400390625, 2887845039367675781250, 186601230428607421875000, 12146710229056792968750000, 795792421294273872070312500

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^8 )^(1/5).

a(n) = 25^n * binomial(8*n/5+1/5,n)/(8*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^11).

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(8/5)) )^(1/8).

a(n) ~ 2^((24*n-7)/5) * 5^n / (3^((6*n+7)/10) * n^(3/2) * sqrt(Pi)). - Amiram Eldar, Nov 25 2025

Mathematica

a[n_] := 25^n * Binomial[8*n/5 + 1/5, n]/(8*n + 1); Array[a, 17, 0] (* Amiram Eldar, Nov 25 2025 *)

Prog

(PARI) a(n) = 25^n*binomial(8*n/5+1/5, n)/(8*n+1);

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380465, A380471.

Sequence in context: A230666 A113560 A094364 * A232788 A324097 A082441

Adjacent sequences: A380463 A380464 A380465 * A380467 A380468 A380469

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2025

Status

approved