A248978 Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + ... + x^n to the polynomial A_k*(x-3k)^k for 0 <= k <= n.
1, 4, 1, 4, 13, 1, 4, 94, 28, 1, 4, 526, 460, 49, 1, 4, 2551, 5860, 1399, 76, 1, 4, 11299, 64180, 30559, 3316, 109, 1, 4, 47020, 635716, 566374, 109156, 6724, 148, 1, 4, 186988, 5861188, 9384358, 3012196, 309124, 12244, 193, 1, 4, 718429, 51210820, 143307490, 73556068, 11790874, 747076, 20605, 244, 1, 4, 2686729, 429124420, 2056495090, 1641197668, 394515874, 37488676, 1608205, 32644, 301, 1
Offset: 0
Examples
1; 4, 1; 4, 13, 1; 4, 94, 28, 1; 4, 526, 460, 49, 1; 4, 2551, 5860, 1399, 76, 1; 4, 11299, 64180, 30559, 3316, 109, 1; 4, 47020, 635716, 566374, 109156, 6724, 148, 1; 4, 186988, 5861188, 9384358, 3012196, 309124, 12244, 193, 1; 4, 718429, 51210820, 143307490, 73556068, 11790874, 747076, 20605, 244, 1;
Programs
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PARI
for(n=0, 10, for(k=0, n, if(!k, if(n, print1(4, ", ")); if(!n, print1(1, ", "))); if(k, print1(sum(i=1, n, ((3*k)^(i-k)*i*binomial(i,k)))/k, ", "))))
Formula
T(n,n-1) = 1 + 3n^2 for n > 0.
T(n,1) = (3^n*(n^2-n+1)-1)/2 for n > 0.
Comments