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A104030 Matrix inverse, read by rows, of triangle A104029, which forms the pairwise sums of trinomial coefficients. 4

%I

%S 1,-2,1,7,-5,1,-41,32,-9,1,376,-299,91,-14,1,-5033,4015,-1241,205,-20,

%T 1,92821,-74080,22954,-3842,400,-27,1,-2257166,1801537,-558402,93652,

%U -9863,707,-35,1,69981919,-55855829,17313721,-2904530,306409,-22190,1162,-44,1,-2694447797,2150565968

%N Matrix inverse, read by rows, of triangle A104029, which forms the pairwise sums of trinomial coefficients.

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

%C Row sums equal negative Genocchi numbers of first kind (A001469).

%C Rows form polynomials R_n(x) such that: R_n(3) = 1 for n>=0 and R_n(1/2) = (-1)^n*A005647(n+1)/2^n (signed Salie numbers).

%C Column 1 forms A104031.

%C Unsigned row sums form A104032.

%e Rows begin:

%e 1;

%e -2,1;

%e 7,-5,1;

%e -41,32,-9,1;

%e 376,-299,91,-14,1;

%e -5033,4015,-1241,205,-20,1;

%e 92821,-74080,22954,-3842,400,-27,1;

%e -2257166,1801537,-558402,93652,-9863,707,-35,1; ...

%o (PARI) T(n,k)=if(n<k || k<0,0,((matrix(n+2,n+2,m,j,if(m>=j, polcoeff((1+x+x^2)^(m-1)+O(x^(2*j)),2*j-2)+ polcoeff((1+x+x^2)^(m-1)+O(x^(2*j)),2*j-1))))^-1)[n+1,k+1])

%Y Cf. A006846, A001469, A005647, A104027, A104029, A104031, A104032.

%K sign,tabl

%O 0,2

%A _Paul D. Hanna_, Feb 26 2005

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Last modified September 25 13:37 EDT 2021. Contains 347654 sequences. (Running on oeis4.)