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A102222 Logarithm of triangular matrix A102220, which equals [2*I - A008459]^(-1).

%I A102222 #8 Jul 19 2024 19:05:03
%S A102222 0,1,0,3,4,0,22,27,9,0,323,352,108,16,0,7906,8075,2200,300,25,0,
%T A102222 290262,284616,72675,8800,675,36,0,14919430,14222838,3486546,395675,
%U A102222 26950,1323,49,0,1022475715,954843520,227565408,24793216,1582700,68992,2352,64,0
%N A102222 Logarithm of triangular matrix A102220, which equals [2*I - A008459]^(-1).
%C A102222 Column 0 forms A102223.
%F A102222 T(n, k) = C(n, k)^2*A102223(n-k). T(n, 0) = A102223(n). T(n, n) = 0 for n>=0. [A102222] = Sum_{m=1..inf} [A008459 - I]^m/m.
%e A102222 Rows begin:
%e A102222 [0],
%e A102222 [1,0],
%e A102222 [3,4,0],
%e A102222 [22,27,9,0],
%e A102222 [323,352,108,16,0],
%e A102222 [7906,8075,2200,300,25,0],
%e A102222 [290262,284616,72675,8800,675,36,0],...
%e A102222 which equals the term-by-term product of column 0
%e A102222 with the squared binomial coefficients (A008459):
%e A102222 [(0)1^2],
%e A102222 [(1)1^2,(0)1^2],
%e A102222 [(3)1^2,(1)2^2,(0)1^2],
%e A102222 [(22)1^2,(3)3^2,(1)3^2,(0)1^2],
%e A102222 [(323)1^2,(22)4^2,(3)6^2,(1)4^2,(0)1^2],...
%o A102222 (PARI) {T(n,k)=if(n<k||k<0,0,sum(m=1,n, (matrix(n+1,n+1,i,j,binomial(i-1,j-1)^2-if(i==j,1,0))^m/m)[n+1,k+1]))}
%Y A102222 Cf. A008459, A102220, A102223.
%K A102222 nonn,tabl
%O A102222 0,4
%A A102222 _Paul D. Hanna_, Dec 31 2004