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G.f.: tzt*z*(1+z)/[((1-z)^3-tzt*z*(1+z)]).
From Vladimir Kruchinin, Nov 25 2011: (Start)
G.f.: ((x+x^2)/(1-x)^3)^k = Sum_{n>=k} T(n,k)*x^n.
G.f.: [(x+x^2)/(1-x)^3]^k=sum(n>=k, T(n,k)*x^n). T(n,k) =sum( Sum{i=0..n-k, } binomial(k,i)*binomial(n+2*k-i-1,3*k-1)). [_Vladimir Kruchinin_, Nov 25 2011](End)
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1;
4,1;
9,8,1;
16,34,12,1;
25,104,75,16,1;
...
1
0, 1
0, 4, 1
0, 9, 8, 1
0, 16, 34, 12, 1
0, 25, 104, 75, 16, 1
...
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T(n, k):=sum(binomial(k, i)*binomial(n+2*k-i-1, 3*k-1), i, 0, n-k); \\ _/* _Vladimir Kruchinin_, Nov 25 2011 */
(SageSageMath)
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