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

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.

Links

Table of n, a(n) for n=0..46.

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])

Crossrefs

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

Sequence in context: A248811 A048505 A124821 * A206533 A262057 A082791

Adjacent sequences: A104027 A104028 A104029 * A104031 A104032 A104033

Keyword

sign,tabl

Author

Paul D. Hanna, Feb 26 2005

Status

approved