A379086 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n+k,n-2*k).
1, 3, 21, 174, 1509, 13443, 121962, 1120899, 10401021, 97230090, 914283621, 8638552464, 81945757734, 779949538176, 7444735446813, 71237074583589, 683125330952205, 6563268117869076, 63164380112090814, 608805362150884731, 5875874727915635409, 56780302474503539427, 549294315060885105744
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\2, binomial(3*n+k-1, k)*binomial(3*n+k, n-2*k));
Formula
a(n) = [x^n] 1/( 1/(1 + x) - x^2 )^(3*n).
a(n) == 0 (mod 3) for n>0.