A320907 Row sums of A320906.
0, 1, 7, 33, 130, 461, 1525, 4802, 14577, 43025, 124226, 352437, 985821, 2725858, 7466185, 20291193, 54791842, 147164525, 393517477, 1048395650, 2784568545, 7377137441, 19503081602, 51470797413, 135641216685, 357029910946, 938837513785, 2466747164937
Offset: 0
Keywords
Programs
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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 *)
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