%I A102220
%S A102220 1,1,1,5,4,1,55,45,9,1,1077,880,180,16,1,32951,26925,5500,500,25,1,
%T A102220 1451723,1186236,242325,22000,1125,36,1,87054773,71134427,14531391,
%U A102220 1319325,67375,2205,49,1,6818444405,5571505472,1138150832,103334336
%N A102220 Triangular matrix, read by rows, equal to [2*I - A008459]^(-1), i.e., 
               the matrix inverse of the difference of twice the identity matrix 
               and the triangular matrix of squared binomial coefficients.
%C A102220 Column 0 forms A102221. Row sums form twice column 0 for n>0. Matrix 
               logarithm is A102222.
%F A102220 T(n, k) = C(n, k)^2*A102221(n-k). T(n, 0) = A102221(n). 2*A102221(n) 
               = Sum_{k=0, n} T(n, k) for n>0.
%e A102220 Rows begin:
%e A102220 [1],
%e A102220 [1,1],
%e A102220 [5,4,1],
%e A102220 [55,45,9,1],
%e A102220 [1077,880,180,16,1],
%e A102220 [32951,26925,5500,500,25,1],
%e A102220 [1451723,1186236,242325,22000,1125,36,1],...
%e A102220 and equal the term-by-term product of column 0
%e A102220 with the squared binomial coefficients (A008459):
%e A102220 [(1)1^2],
%e A102220 [(1)1^2,(1)1^2],
%e A102220 [(5)1^2,(1)2^2,(1)1^2],
%e A102220 [(55)1^2,(5)3^2,(1)3^2,(1)1^2],
%e A102220 [(1077)1^2,(55)4^2,(5)6^2,(1)4^2,(1)1^2],...
%e A102220 The matrix inverse is [2*I - A008459]:
%e A102220 [1],
%e A102220 [ -1,1],
%e A102220 [ -1,-4,1],
%e A102220 [ -1,-9,-9,1],
%e A102220 [ -1,-16,-36,-16,1],...
%o A102220 (PARI) {T(n,k)=(matrix(n+1,n+1,i,j,if(i==j,2,0)-binomial(i-1,j-1)^2)^-1)[n+1,
               k+1]}
%Y A102220 Cf. A008459, A102221, A102222.
%Y A102220 Sequence in context: A008955 A152862 A108440 this_sequence A109430 A085917 
               A102593
%Y A102220 Adjacent sequences: A102217 A102218 A102219 this_sequence A102221 A102222 
               A102223
%K A102220 nonn,tabl
%O A102220 0,4
%A A102220 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2004