OFFSET
0,3
COMMENTS
Image of n^3 under the mapping of g(x)->(1/sqrt(1-4x^2))g(xc(x^2)) where c(x) is the g.f. of A000108.
FORMULA
G.f.: 4x(sqrt(1-4x^2)-1)^2(4x+1)/(sqrt(1-4x^2)(sqrt(1-4x^2)+2x-1)^4); a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*(n-2k)^3.
D-finite with recurrence (n-1)*a(n)+4*(n-4)*a(n-1) -4*(n+4)*a(n-2) +16*(2-n)*a(n-3)=0. - R. J. Mathar, Nov 09 2012
From Vaclav Kotesovec, Nov 04 2017: (Start)
G.f.: x*(1 + 4*x) / ((1 - 2*x)^(5/2) * sqrt(1 + 2*x)).
a(n) ~ 2^(n + 1/2) * n^(3/2) / sqrt(Pi). (End)
MATHEMATICA
CoefficientList[Series[x*(1 + 4*x) / ((1 - 2*x)^(5/2) * Sqrt[1 + 2*x]), {x, 0, 30}], x] (* Vaclav Kotesovec, Nov 04 2017 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 13 2005
STATUS
approved