A049393 Expansion of (1-25*x)^(1/5).

1, -5, -50, -750, -13125, -249375, -4987500, -103312500, -2195390625, -47566796875, -1046469531250, -23307730468750, -524423935546875, -11900389306640625, -272008898437500000, -6256204664062500000, -144674732856445312500, -3361559969311523437500

Offset: 0

Author

Joe Keane (jgk(AT)jgk.org)

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A049382.

Programs

Maple

A049393 := proc(n)
    coeftayl((1-25*x)^(1/5), x=0, n);
end proc:
seq(A049393(n), n=0..20); # Wesley Ivan Hurt, Jul 13 2014

Mathematica

CoefficientList[Series[(1 - 25 x)^(1/5), {x, 0, 20}], x] (* Wesley Ivan Hurt, Jul 13 2014 *)

PARI

Vec(taylor((1-25*x)^(1/5), x, 40)) \\ Michel Marcus, Jul 16 2014

Formula

G.f.: (1-25*x)^(1/5).

a(n) = 5^n/n! * product[ k=0..n-1 ] (5*k-1).

a(n) ~ -1/5*Gamma(4/5)^-1*n^(-6/5)*5^(2*n)*{1 + 3/25*n^-1 + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001