A104417 Triangle, read by rows, equal to the matrix inverse of A104416, where A104416(n,k) = A008275(k+1,n-k+1) (Stirling numbers of the first kind).
1, 1, 1, 3, 3, 1, 16, 16, 6, 1, 127, 127, 49, 10, 1, 1363, 1363, 531, 115, 15, 1, 18628, 18628, 7286, 1615, 230, 21, 1, 311250, 311250, 121964, 27321, 4040, 413, 28, 1, 6173791, 6173791, 2421471, 545311, 82131, 8841, 686, 36, 1, 142190703, 142190703
Offset: 0
Examples
Column 0 forms A082161 that satisfies: 1 = (1-x) + 1*x*(1-x)(1-2x) + 3*x^2*(1-x)(1-2x)(1-3x) + + 16*x^3*(1-x)(1-2x)(1-3x)(1-4x) + ... + A082161(n+1)*x^n*(1-x)(1-2x)(1-3x)*..*(1-(n+1)*x) + ... this g.f. can be derived from the matrix inverse, A104416. Rows begin: 1; 1,1; 3,3,1; 16,16,6,1; 127,127,49,10,1; 1363,1363,531,115,15,1; 18628,18628,7286,1615,230,21,1; 311250,311250,121964,27321,4040,413,28,1; ...
Programs
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PARI
Comments