A379085 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(2*n+k,n-3*k).
1, 2, 6, 26, 142, 802, 4434, 24222, 132686, 733076, 4081926, 22853052, 128427106, 723862856, 4090573570, 23170106086, 131515806574, 747875338152, 4259810283828, 24298797944956, 138787172202182, 793651842511512, 4543393775520936, 26035130683198684, 149325002408646002
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(2*n+k-1, k)*binomial(2*n+k, n-3*k));
Formula
a(n) = [x^n] 1/( 1/(1 + x) - x^3 )^(2*n).
a(n) == 0 (mod 2) for n>0.