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A104030
Matrix inverse, read by rows, of triangle A104029, which forms the pairwise sums of trinomial coefficients.
4
1, -2, 1, 7, -5, 1, -41, 32, -9, 1, 376, -299, 91, -14, 1, -5033, 4015, -1241, 205, -20, 1, 92821, -74080, 22954, -3842, 400, -27, 1, -2257166, 1801537, -558402, 93652, -9863, 707, -35, 1, 69981919, -55855829, 17313721, -2904530, 306409, -22190, 1162, -44, 1, -2694447797, 2150565968
OFFSET
0,2
COMMENTS
Column 0 forms signed Hammersley's polynomial p_n(1) (A006846), offset 1.
Row sums equal negative Genocchi numbers of first kind (A001469).
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).
Column 1 forms A104031.
Unsigned row sums form A104032.
EXAMPLE
Rows begin:
1;
-2,1;
7,-5,1;
-41,32,-9,1;
376,-299,91,-14,1;
-5033,4015,-1241,205,-20,1;
92821,-74080,22954,-3842,400,-27,1;
-2257166,1801537,-558402,93652,-9863,707,-35,1; ...
PROG
(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])
KEYWORD
sign,tabl
AUTHOR
Paul D. Hanna, Feb 26 2005
STATUS
approved