a(n,m) tabf head (staircase) for A128502
First convolution of Chebyshev S-polynomials
sum(S(n-k,x)*S(k,x),k=0..n)= sum(a(n,m)*x^(n-2*m) ,m=0..floor(n/2)).
The row length sequence of this array is [1,1,2,2,3,3,4,4,...]=A004526.
n\m 0 1 2 3 4 5 6 7 ...
0 1 0 0 0 0 0 0 0
1 2 0 0 0 0 0 0 0
2 3 -2 0 0 0 0 0 0
3 4 -6 0 0 0 0 0 0
4 5 -12 3 0 0 0 0 0
5 6 -20 12 0 0 0 0 0
6 7 -30 30 -4 0 0 0 0
7 8 -42 60 -20 0 0 0 0
8 9 -56 105 -60 5 0 0 0
9 10 -72 168 -140 30 0 0 0
10 11 -90 252 -280 105 -6 0 0
11 12 -110 360 -504 280 -42 0 0
12 13 -132 495 -840 630 -168 7 0
13 14 -156 660 -1320 1260 -504 56 0
14 15 -182 858 -1980 2310 -1260 252 -8
15 16 -210 1092 -2860 3960 -2772 840 -72
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G.f. for column m sequences: ((-1)^m)*(m+1)*(x^(2*m))/(1-x)^(m+2), m>=0.
The column sequences, divided by (m+1)*(-1)^m coincide with the columns m+1 of
Pascal's triangle.
Row polynomials P(n,x):= sum(a(n,m)*x^n,m=0..floor(n/2)) (increasing powers of x)
are generated by 1/(1-z-x*z^2)^2.
The convolution polynomials S1(n,x):=sum(S(n-k,x)*S(k,x),k=0..n)=
sum(a(n,m)*x^(n-2*m),m=0..floor(n/2)) are generated by 1/(1-x*z+z^2)^2.
Row sums (signed) are: [1, 2, 1, -2, -4, -2, 3, 6, 3, -4, -8, -4, 5, 10, 5, -6,...]
= A099254(n), n>=0.
G.f.: 1/(1-x+x^2)^2 (convolution of the period 6 sequence A099254).
Row sums (unsigned) are:
[1, 2, 5, 10, 20, 38, 71, 130, 235, 420, 744, 1308, 2285, 3970, 6865, 11822,...]
= A001629(n+2),n>=0.
G.f.: 1/(1-x-x^2)^2 (Fibonacci convolution A001629).
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