OFFSET
0,3
FORMULA
a(n) = n*sum(k=1..n, (binomial(2*k,n-k)*binomial(n-k-1,k-1))/k, n>0, a(0)=1.
D-finite with recurrence: 3*n*a(n) +(7*n-8)*a(n-1) +2*(-3*n-2)*a(n-2) +2*(-19*n+35)*a(n-3) +2*(-26*n+81)*a(n-4) +4*(-8*n+35)*a(n-5) +4*(-2*n+11)*a(n-6)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
CoefficientList[Series[(2 x^2 + 4 x + 3) / ((2 x + 2) Sqrt[-4 x^3 - 4 x^2 + 1]) - 1 / (2 x + 2), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)
PROG
(Maxima)
a(n):=if n=0 then 1 else n*sum((binomial(2*k, n-k)*binomial(n-k-1, k-1))/k, k, 1, n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Nov 22 2014
STATUS
approved