OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1-sqrt(1-4*x^4/(1-x)^4)) / (2*x^4*(1-x)).
a(n) = ((n+4)/4) * Sum_{k=0..(n+4)/4} (binomial(2*k,k)*binomial(n+3,n-4*k)/(k+1)^2).
a(n) ~ (1+sqrt(2))^(n+11/2) / (2^(7/4)*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 23 2016
D-finite with recurrence: (n+4)*a(n) +(-6*n-19)*a(n-1) +5*(3*n+7)*a(n-2) +10*(-2*n-3)*a(n-3) +(11*n+18)*a(n-4) +(2*n-11)*a(n-5) +3*(-n+1)*a(n-6)=0. - R. J. Mathar, Jun 07 2016
MATHEMATICA
CoefficientList[Series[1/(1 - x) (1 - Sqrt[1 - 4 x^4/(1 - x)^4])/(2 x^4), {x, 0, 30}], x] (* or *) Table[(n + 4)/4 Sum[Binomial[2 k, k] Binomial[n + 3, n - 4 k]/(k + 1)^2, {k, 0, (n + 4)/4}], {n, 0, 30}] (* Michael De Vlieger, Mar 23 2016 *)
PROG
(Maxima) a(n):=((n+4)/4*sum((binomial(2*k, k)*binomial(n+3, n-4*k))/(k+1)^2, k, 0, (n+4)/4));
(PARI) x='x+O('x^44); Vec((1-sqrt(1-4*x^4/(1-x)^4))/(2*x^4*(1-x))) \\ Altug Alkan, Mar 23 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 23 2016
STATUS
approved