OFFSET
0,3
FORMULA
a(n)= (2(2n-1)/(n-1))*a(n-1) - (16n/(n-1))*a(n-2), starting with a(0) = 0 and a(1) = 1. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 15 2004
For n > 0, a(n) = (n+1)*A025175(n-1)/2. - Vladimir Reshetnikov, Nov 01 2015
MAPLE
MATHEMATICA
Table[ -((2^(-1 + 2*n)*LegendreP[ n, 1, 1/2 ])/Sqrt[ 3 ]), {n, 0, 12} ]
Table[4^n (n+1) (LegendreP[n, 1/2] - 2 LegendreP[n+1, 1/2])/6, {n, 0, 20}] (* Vladimir Reshetnikov, Nov 01 2015 *)
CoefficientList[Series[x/(1-4x+16x^2)^(3/2), {x, 0, 30}], x] (* Harvey P. Dale, May 07 2021 *)
PROG
(PARI) x='x+O('x^50); concat(0, Vec(x/(1-4*x+16*x^2)^(3/2))) \\ Altug Alkan, Nov 02 2015
(PARI) a(n) = 4^n*(n+1)*(pollegendre(n, 1/2) -2*pollegendre(n+1, 1/2))/6; \\ Michel Marcus, Nov 03 2015
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Simpler definition and more terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 15 2004
STATUS
approved