cp's OEIS Frontend

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).

%I A104417 #3 Mar 30 2012 18:36:45
%S A104417 1,1,1,3,3,1,16,16,6,1,127,127,49,10,1,1363,1363,531,115,15,1,18628,
%T A104417 18628,7286,1615,230,21,1,311250,311250,121964,27321,4040,413,28,1,
%U A104417 6173791,6173791,2421471,545311,82131,8841,686,36,1,142190703,142190703
%N 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).
%C A104417 Column 0 and column 1 contain A082161.
%e A104417 Column 0 forms A082161 that satisfies:
%e A104417 1 = (1-x) + 1*x*(1-x)(1-2x) + 3*x^2*(1-x)(1-2x)(1-3x) +
%e A104417 + 16*x^3*(1-x)(1-2x)(1-3x)(1-4x) + ...
%e A104417 + A082161(n+1)*x^n*(1-x)(1-2x)(1-3x)*..*(1-(n+1)*x) + ...
%e A104417 this g.f. can be derived from the matrix inverse, A104416.
%e A104417 Rows begin:
%e A104417 1;
%e A104417 1,1;
%e A104417 3,3,1;
%e A104417 16,16,6,1;
%e A104417 127,127,49,10,1;
%e A104417 1363,1363,531,115,15,1;
%e A104417 18628,18628,7286,1615,230,21,1;
%e A104417 311250,311250,121964,27321,4040,413,28,1; ...
%o A104417 (PARI)
%Y A104417 Cf. A104416, A082161.
%K A104417 nonn,tabl
%O A104417 0,4
%A A104417 _Paul D. Hanna_, Mar 06 2005