cp's OEIS Frontend

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

%I A104030 #10 Jun 13 2017 01:28:38
%S A104030 1,-2,1,7,-5,1,-41,32,-9,1,376,-299,91,-14,1,-5033,4015,-1241,205,-20,
%T A104030 1,92821,-74080,22954,-3842,400,-27,1,-2257166,1801537,-558402,93652,
%U A104030 -9863,707,-35,1,69981919,-55855829,17313721,-2904530,306409,-22190,1162,-44,1,-2694447797,2150565968
%N A104030 Matrix inverse, read by rows, of triangle A104029, which forms the pairwise sums of trinomial coefficients.
%C A104030 Column 0 forms signed Hammersley's polynomial p_n(1) (A006846), offset 1.
%C A104030 Row sums equal negative Genocchi numbers of first kind (A001469).
%C A104030 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 A104030 Column 1 forms A104031.
%C A104030 Unsigned row sums form A104032.
%e A104030 Rows begin:
%e A104030 1;
%e A104030 -2,1;
%e A104030 7,-5,1;
%e A104030 -41,32,-9,1;
%e A104030 376,-299,91,-14,1;
%e A104030 -5033,4015,-1241,205,-20,1;
%e A104030 92821,-74080,22954,-3842,400,-27,1;
%e A104030 -2257166,1801537,-558402,93652,-9863,707,-35,1; ...
%o A104030 (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 A104030 Cf. A006846, A001469, A005647, A104027, A104029, A104031, A104032.
%K A104030 sign,tabl
%O A104030 0,2
%A A104030 _Paul D. Hanna_, Feb 26 2005