A006846 -id:A006846 - cp's OEIS frontend

A104031 Column 1 of triangle A104030, which is the matrix inverse of the triangle of pairwise sums of trinomial coefficients.

1, -5, 32, -299, 4015, -74080, 1801537, -55855829, 2150565968, -100668835739, 5630336915071, -370807060847872, 28403381397111649, -2503741873703550533, 251652633457563092096, -28608467296650576313259, 3652291148549164761101551, -520296573821474451201241696

Offset: 0

Paul D. Hanna, Feb 26 2005

sign

Column 0 of triangle A104030 forms signed Hammersley's polynomial p_n(1) (A006846), offset 1.

Cf. A104030.

{a(n)=if(n<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+2,2])}

A259908 Triangle read by rows: Hammersley's numbers c_{j,k} arising from a formula for A085707(n,k).

Original entry on oeis.org

1, 3, 5, 17, 70, 61, 155, 1143, 2317, 1385, 2073, 23716, 82286, 110556, 50521, 38227, 623753, 3243270, 7258090, 7293671, 2702765, 929569, 20454498, 147624355, 484343420, 796220487, 639139202, 199360981

Offset: 1

N. J. A. Sloane, Jul 07 2015

			Triangle begins:
       1,
       3,        5,
      17,       70,        61,
     155,     1143,      2317,      1385,
    2073,    23716,     82286,    110556,     50521,
   38227,   623753,   3243270,   7258090,   7293671,   2702765,
  929569, 20454498, 147624355, 484343420, 796220487, 639139202, 199360981,
  ...

J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23. See Eq. (52) and Table 2.
J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23. (Annotated scanned copy)

Cf. A085707.

Diagonals are A001469, A000364.

Missing row 5 added by Michel Marcus, Feb 07 2023

cp's OEIS Frontend

A104031 Column 1 of triangle A104030, which is the matrix inverse of the triangle of pairwise sums of trinomial coefficients.

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A259908 Triangle read by rows: Hammersley's numbers c_{j,k} arising from a formula for A085707(n,k).

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