A385203 G.f. A(x) satisfies A(x) = ( 1 + 25*x*A(x)^2 )^(1/5).

1, 5, 0, -125, 625, 5625, -87500, 0, 9140625, -60156250, -653125000, 11654296875, 0, -1470068359375, 10353515625000, 118916992187500, -2225148925781250, 0, 302784667968750000, -2199076690673828125, -25952287445068359375, 497460246276855468750, 0

Offset: 0

Author

Seiichi Manyama, Jun 21 2025

Keywords

• sign

Crossrefs

Cf. A078534, A385204, A385205.

Programs

PARI

a(n) = 25^n*binomial(2*n/5+1/5, n)/(2*n+1);

Formula

a(n) = 25^n * binomial(2*n/5+1/5,n)/(2*n+1).

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

G.f.: ( (1/x) * Series_Reversion(x/(1+25*x)^(2/5)) )^(1/2).

a(5*n+2) = 0 for n >= 0.