%I A118193
%S A118193 1,1,4,76,7124,3326876,7760553124,90490361296876,5275336666748203124,
%T A118193 1537656615631182860546876,2240970675863910673065189453124,
%U A118193 16329855533286908545970966339091796876,594974481262862479448134839533519744970703124
%V A118193 1,-1,4,-76,7124,-3326876,7760553124,-90490361296876,5275336666748203124,
%W A118193 -1537656615631182860546876,2240970675863910673065189453124,
%X A118193 -16329855533286908545970966339091796876,594974481262862479448134839533519744970703124
%N A118193 Column 0 of the matrix inverse of triangle A118190(n,k) = (5^k)^(n-k).
%C A118193 The entire matrix inverse of triangle A118193 is determined by column 
               0 (this sequence): [A118190^-1](n,k) = a(n-k)*(5^k)^(n-k) for n>=k>
               =0. Any g.f. of the form: Sum_{k>=0} b(k)*x^k may be expressed as: 
               Sum_{n>=0} c(n)*x^n/(1-5^n*x) by applying the inverse transformation: 
               c(n) = Sum_{k=0..n} a(n-k)*b(k)*(5^k)^(n-k).
%F A118193 G.f.: 1 = Sum_{n>=0} a(n)*x^n/(1-5^n*x). 0^n = Sum_{k=0..n} a(k)*(5^k)^(n-k) 
               for n>=0.
%e A118193 Recurrence at n=4:
%e A118193 0 = a(0)*(5^0)^4 +a(1)*(5^1)^3 +a(2)*(5^2)^2 +a(3)*(5^3)^1 +a(4)*(5^4)^0
%e A118193 = 1*(5^0) - 1*(5^3) + 4*(5^4) - 76*(5^3) + 7124*(5^0).
%e A118193 The g.f. is illustrated by:
%e A118193 1 = 1/(1-x) - 1*x/(1-5*x) + 4*x^2/(1-25*x) - 76*x^3/(1-125*x) +
%e A118193 7124*x^4/(1-625*x) - 3326876*x^5/(1-3125*x) + 7760553124*x^6/(1-15625*x) 
               +...
%o A118193 (PARI) {a(n)=local(T=matrix(n+1,n+1,r,c,if(r>=c,(5^(c-1))^(r-c)))); return((T^-1)[n+1,
               1])}
%Y A118193 Cf. A118190.
%Y A118193 Sequence in context: A012047 A012010 A012155 this_sequence A052271 A080989 
               A006267
%Y A118193 Adjacent sequences: A118190 A118191 A118192 this_sequence A118194 A118195 
               A118196
%K A118193 sign
%O A118193 0,3
%A A118193 Paul D. Hanna (pauldhanna(AT)juno.com), Apr 15 2006