OFFSET
0,2
FORMULA
G.f.: A(x) = sqrt( (1+2x)/(1-2x)^3 ).
a(n) = Sum_{k=0..[(n+1)/2]} C(n+1, k)*(n+1-2k)^3/(n+1).
a(n) = A107233(n)/(n+1).
Self-convolution equals A014477.
E.g.f.: ((1 + 4*x)*BesselI(0, 2*x) + 4*x*BesselI(1, 2*x)). - Peter Luschny, Aug 26 2012
MATHEMATICA
CoefficientList[Series[Sqrt[(1+2x)/(1-2x)^3], {x, 0, 30}], x] (* Harvey P. Dale, Jan 04 2016 *)
PROG
(PARI) a(n)=sum(k=0, floor((n+1)/2), binomial(n+1, k)*(n+1-2*k)^3)/(n+1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 14 2008
STATUS
approved