A380471 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^4 )^(1/5).

1, 5, 175, 8625, 495000, 30980625, 2050781250, 141187921875, 10006590468750, 725240531640625, 53503504196484375, 4004478454589843750, 303320955472031250000, 23207794539155419921875, 1791025435519151367187500, 139250846557940616210937500, 10897102765738964080810546875

Offset: 0

Author

Seiichi Manyama, Jun 23 2025

Keywords

• nonn

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380465, A380466.

Programs

PARI

a(n) = 25^n*binomial(9*n/5+1/5, n)/(9*n+1);

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^9 )^(1/5).

a(n) = 25^n * binomial(9*n/5+1/5,n)/(9*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^13).

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(9/5)) )^(1/9).