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

Author

Seiichi Manyama, Jun 23 2025

Keywords

• nonn

Crossrefs

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

Programs

PARI

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

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).