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A080419 Triangle of generalized Chebyshev coefficients.

%I A080419 #8 Apr 15 2018 13:27:31
%S A080419 1,4,1,15,7,1,54,36,10,1,189,162,66,13,1,648,675,360,105,16,1,2187,
%T A080419 2673,1755,675,153,19,1,7290,10206,7938,3780,1134,210,22,1,24057,
%U A080419 37908,34020,19278,7182,1764,276,25,1,78732,137781,139968,91854,40824,12474,2592
%N A080419 Triangle of generalized Chebyshev coefficients.
%C A080419 Second binomial transform of 'pruned' Pascal triangle Binomial(i+1,j+1), (i,j>=0).
%F A080419 T(n,1) = A006234(n+2), T(n,n) = 1, T(n,k) = T(n-1,k-1) + 3*T(n-1,k), T(n,k)=0 for k>n. - corrected by _Michel Marcus_, Apr 15 2018
%F A080419 As a square array, T1(n, k)= (n+3k)3^n Product{j=1..(k-1), n+j}/(3k(k-1)!) (k>=1, n>=0).
%e A080419 Rows are:
%e A080419 {1},
%e A080419 {4,1},
%e A080419 {15,7,1},
%e A080419 {54,36,10,1},
%e A080419 {189,162,66,13,1},
%e A080419 ...
%e A080419 For example, 10 = 7+3*1, 66 = 36+3*10.
%o A080419 (PARI) T(n, k) = if (k==1, (n+2)*3^(n-2), if (k==n, 1, if (k < n, T(n-1, k-1) + 3*T(n-1, k), 0)));
%o A080419 tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Apr 15 2018
%Y A080419 Columns include A006234, A080420, A080421, A080422, A080423.
%K A080419 easy,nonn,tabl
%O A080419 1,2
%A A080419 _Paul Barry_, Feb 19 2003