OFFSET
0,3
COMMENTS
Motzkin transform of the squares.
FORMULA
a(n) = Sum_{k=0..n} k^2*binomial(n, k)*hypergeom([(k-n)/2, (k-n+1)/2], [k+2], 4).
a(n) ~ 4 * 3^(n - 1/2) * sqrt(n/Pi) * (1 - sqrt(3*Pi/n)/2). - Vaclav Kotesovec, May 24 2021
D-finite with recurrence -(n+1)*(2*n-3)*a(n) +(10*n^2-5*n-12)*a(n-1) -3*(2*n+5)*(n-1)*a(n-2) -9*(2*n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Mar 06 2022
MAPLE
gf := ((x - 1)/sqrt(4/(x + 1) - 3) + x + 1)/(2*x*(3*x - 1)):
ser := series(gf, x, 30): seq(coeff(ser, x, n), n=0..27);
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, May 23 2021
STATUS
approved