A104986 Matrix logarithm of triangle A104980.

0, 1, 0, 2, 2, 0, 7, 4, 3, 0, 33, 14, 7, 4, 0, 191, 66, 27, 11, 5, 0, 1297, 382, 137, 48, 16, 6, 0, 10063, 2594, 843, 270, 79, 22, 7, 0, 87669, 20126, 6041, 1820, 495, 122, 29, 8, 0, 847015, 175338, 49219, 14176, 3679, 848, 179, 37, 9, 0, 8989301, 1694030, 448681, 124828, 31361, 6930, 1371, 252, 46, 10, 0

Offset: 0

Author

Paul D. Hanna, Apr 10 2005

Keywords

• nonn
• tabl

Comments

Column 0 equals column 1 of triangular matrix A104980, which satisfies: SHIFT_LEFT(column 0 of A104980^p) = p*(column p+1 of A104980) for p>=0. Column 1 equals twice column 0.

Examples

			Triangle begins:
        0;
        1,       0;
        2,       2,      0;
        7,       4,      3,      0;
       33,      14,      7,      4,     0;
      191,      66,     27,     11,     5,    0;
     1297,     382,    137,     48,    16,    6,    0;
    10063,    2594,    843,    270,    79,   22,    7,   0;
    87669,   20126,   6041,   1820,   495,  122,   29,   8,  0;
   847015,  175338,  49219,  14176,  3679,  848,  179,  37,  9,  0;
  8989301, 1694030, 448681, 124828, 31361, 6930, 1371, 252, 46, 10, 0; ...
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A104980, A104981 (column 0), A104987 (row sums).

Programs

Mathematica

nmax = 10;
M = Table[If[n == k, 0, If[n == k+1, -n+1, -Coefficient[(1-1/Sum[i! x^i, {i, 0, n}])/x + O[x]^n, x, n-k-1]]], {n, 1, nmax+1}, {k, 1, nmax+1}];
T[n_, k_] /; 0 <= k <= n := Sum[(-1)^p MatrixPower[M, p][[n+1, k+1]]/p, {p, 1, n+1}]; T[, ] = 0;
Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 09 2018, from PARI *)

PARI

T(n,k)=if(n
				

Formula

T(n, 0) = A104981(n), T(n+1, 1) = 2*T(n, 0) for n>=0.