OFFSET
0,2
FORMULA
a(0) = 1, a(1) = 10; a(n) = (2*(2*n+3)*a(n-1) + 4*(n+3)*a(n-2))/n.
a(n) = (binomial(n+4,2)/6) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(n+2,n-2*k) * binomial(2*k+2,k).
a(n) = 2^(n-3)*Pochhammer(n+1, 4)*hypergeom([(1-n)/2, -n/2], [3], 2)/3. - Stefano Spezia, Jul 10 2024
a(n) = Sum_{k=0..n} (-4)^k * binomial(-5/2,k) * binomial(k,n-k). - Seiichi Manyama, Oct 19 2024
MATHEMATICA
a[n_]:=2^(n-3) Pochhammer[n+1, 4]*Hypergeometric2F1[(1-n)/2, -n/2, 3, 2]/3; Array[a, 23, 0] (* Stefano Spezia, Jul 10 2024 *)
PROG
(PARI) a(n) = binomial(n+4, 2)/6*sum(k=0, n\2, 2^(n-k)*binomial(n+2, n-2*k)*binomial(2*k+2, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 09 2024
STATUS
approved