cp's OEIS Frontend

A104027 Triangle, read by rows, equal to the matrix inverse of A056241, which is formed from the even-indexed trinomial coefficients.

%I A104027 #10 Jun 13 2017 01:21:16
%S A104027 1,-1,1,2,-3,1,-7,12,-6,1,41,-73,41,-10,1,-376,675,-390,105,-15,1,
%T A104027 5033,-9048,5256,-1446,225,-21,1,-92821,166901,-97034,26796,-4242,427,
%U A104027 -28,1,2257166,-4058703,2359939,-652054,103515,-10570,742,-36,1,-69981919,125837748,-73169550,20218251,-3210939
%N A104027 Triangle, read by rows, equal to the matrix inverse of A056241, which is formed from the even-indexed trinomial coefficients.
%C A104027 Column 0 forms signed Hammersley's polynomial p_n(1) (A006846). Column 1 forms A104028.
%C A104027 Triangle T(n,k), 0<=k<=n, read by rows, given by [ -1, -1, -3, -4, -7, -9, -13, -16, -21, ...] DELTA [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...] where DELTA is the operator defined in A084938; see A004652 : 0, 1, 1, 3, 4, 7, 9, 13, ... - _Philippe Deléham_, Sep 26 2005
%e A104027 Rows begin:
%e A104027 1;
%e A104027 -1,1;
%e A104027 2,-3,1;
%e A104027 -7,12,-6,1;
%e A104027 41,-73,41,-10,1;
%e A104027 -376,675,-390,105,-15,1;
%e A104027 5033,-9048,5256,-1446,225,-21,1;
%e A104027 -92821,166901,-97034,26796,-4242,427,-28,1;
%e A104027 2257166,-4058703,2359939,-652054,103515,-10570,742,-36,1; ...
%o A104027 (PARI) T(n,k)=if(n<k || k<0, 0, ((matrix(n+2,n+2,m,j, if(m && gt;=j,polcoeff((1+x+x^2)^(m-1)+O(x^(2*j)),2*j-2))))^-1)[n+1,k+1])
%Y A104027 Cf. A056241, A104028, A027907.
%K A104027 sign,tabl
%O A104027 0,4
%A A104027 _Paul D. Hanna_, Feb 26 2005