OFFSET
0,2
FORMULA
a(n) = (binomial(n+5,3)/10) * Sum_{k=0..floor(n/2)} binomial(n+2,n-2*k) * binomial(2*k+2,k).
a(n) = (binomial(n+5,3)/10) * A014531(n+1).
a(n) = ((n+5)/(n*(n+4))) * ((2*n+3)*a(n-1) + 3*(n+4)*a(n-2)).
a(n) = (1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*hypergeom([(1-n)/2, -n/2], [3], 4)/120. - Stefano Spezia, Aug 07 2024
MATHEMATICA
a[n_]:=(1+n)(2+n)(3+n)(4+n)(5+n)Hypergeometric2F1[(1-n)/2, -n/2, 3, 4]/120; Array[a, 25, 0] (* Stefano Spezia, Aug 07 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec((1-x)/(1-2*x-3*x^2)^(7/2))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 07 2024
STATUS
approved