OFFSET
0,2
COMMENTS
In general, 1/sqrt((1-a*x)^2-4*b*x^3) expands to sum{k=0..floor(n/2), C(n-k,k)C(n-2k,k)b^k*a^(n-3k)}.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..1837
Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, Diagonal Sums in the Pascal Pyramid, II: Applications, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
FORMULA
a(n)=sum{k=0..floor(n/2), C(n-k, k)C(n-2k, k)2^(n-2k)}.
D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. [Belbachir]
MATHEMATICA
CoefficientList[Series[1/Sqrt[(1-2x)^2-8x^3], {x, 0, 30}], x] (* Harvey P. Dale, Dec 23 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 16 2005
STATUS
approved