OFFSET
0,3
FORMULA
Conjectures from Colin Barker, Oct 28 2018: (Start)
G.f.: x*(1 - x)^2 / ((1 - 2*x)^3*(1 - 3*x + x^2)).
a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>4. (End)
a(n) = Sum_{k=0..n} Sum_{j=0..2*n + 1 - k} binomial(2*n + 1 - k, 2*n + 2 - 2*k + j)*binomial(j + 2, 2). - Detlef Meya, Jan 09 2024
MATHEMATICA
a[n_] := Sum[Sum[Binomial[2*n + 1 - k, 2*n + 2 - 2*k + j]*Binomial[j + 2, 2], {j, 0, 2*n + 1 - k}], {k, 0, n}]; Flatten[Table[a[n], {n, 0, 27}]] (* Detlef Meya, Jan 09 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 28 2018
STATUS
approved