OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} (if (n = k) then 2^n*(2^(n + 1) - 1) else 2^(2*k + 1)*Sum(j, 0..n - k)_ (-1)^j*2^(n - k - j)*binomial(n + 1, j)*binomial(2*n - j - k, n)). - Detlef Meya, Jan 09 2024
a(n) ~ 2^n * 3^(n+1). - Vaclav Kotesovec, Jan 10 2024
MATHEMATICA
a[n_] := Sum[If[n==k, 2^n*(2^(n + 1) - 1), 2^(2*k + 1)*Sum[(-1)^j*2^(n - k - j)*Binomial[n + 1, j]*Binomial[2*n - j - k, n], {j, 0, n-k}]], {k, 0, n}]; Flatten[Table[a[n], {n, 0, 22}]] (* Detlef Meya, Jan 09 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 19 2020
STATUS
approved