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A104027 Triangle, read by rows, equal to the matrix inverse of A056241, which is formed from the even-indexed trinomial coefficients. 5

%I

%S 1,-1,1,2,-3,1,-7,12,-6,1,41,-73,41,-10,1,-376,675,-390,105,-15,1,

%T 5033,-9048,5256,-1446,225,-21,1,-92821,166901,-97034,26796,-4242,427,

%U -28,1,2257166,-4058703,2359939,-652054,103515,-10570,742,-36,1,-69981919,125837748,-73169550,20218251,-3210939

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

%C Column 0 forms signed Hammersley's polynomial p_n(1) (A006846). Column 1 forms A104028.

%C 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 Rows begin:

%e 1;

%e -1,1;

%e 2,-3,1;

%e -7,12,-6,1;

%e 41,-73,41,-10,1;

%e -376,675,-390,105,-15,1;

%e 5033,-9048,5256,-1446,225,-21,1;

%e -92821,166901,-97034,26796,-4242,427,-28,1;

%e 2257166,-4058703,2359939,-652054,103515,-10570,742,-36,1; ...

%o (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 Cf. A056241, A104028, A027907.

%K sign,tabl

%O 0,4

%A _Paul D. Hanna_, Feb 26 2005

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)