A380465 G.f. A(x) satisfies A(x) = 1/( 1 - 25*x*A(x)^2 )^(1/5).

1, 5, 125, 4250, 166250, 7052500, 315459375, 14648437500, 699404062500, 34120414453125, 1693355782421875, 85222795492187500, 4339218139648437500, 223115431527734375000, 11568972340119140625000, 604249120575386718750000, 31761084429202554931640625, 1678825356066226959228515625

Offset: 0

Author

Seiichi Manyama, Jun 23 2025

Keywords

• nonn

Crossrefs

Cf. A034688, A078534, A385203, A385204, A385205, A380466, A380471.

Programs

PARI

a(n) = 25^n*binomial(7*n/5+1/5, n)/(7*n+1);

Formula

G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^7 )^(1/5).

a(n) = 25^n * binomial(7*n/5+1/5,n)/(7*n+1).

G.f. A(x) satisfies A(x) = 1/A(-x*A(x)^9).

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(7/5)) )^(1/7).