A113290 Matrix logarithm of triangle A113287.

0, 2, 0, -3, 0, 0, 6, 4, 4, 0, -10, -10, -10, 0, 0, 19, 24, 30, 12, 6, 0, -35, -49, -70, -42, -21, 0, 0, 72, 104, 164, 128, 84, 24, 8, 0, -150, -216, -360, -324, -252, -108, -36, 0, 0, 343, 480, 820, 800, 710, 400, 180, 40, 10, 0, -803, -1089, -1870, -1892, -1826, -1210, -660, -220, -55, 0, 0

Offset

0,2

Links

Table of n, a(n) for n=0..65.

Formula

T(n, 1) = (n+1)*A113291(n).

Example

Triangle begins:
0;
2,0;
-3,0,0;
6,4,4,0;
-10,-10,-10,0,0;
19,24,30,12,6,0;
-35,-49,-70,-42,-21,0,0;
72,104,164,128,84,24,8,0;
-150,-216,-360,-324,-252,-108,-36,0,0;
343,480,820,800,710,400,180,40,10,0; ...

Prog

(PARI) {T(n, k)=local(x=X+O(X^(n+2)), y=Y+O(Y^(n+2)), M=matrix(n+1, n+1, r, c, if(r==c, 1, if(r>c, r*polcoeff(polcoeff(1/(1-x*y)+x/((1-x*y)*(1+x+x*y)), r-1, X), c-1, Y))))); if(n<k, 0, (sum(j=1, n+1, -(M^0-M)^j/j))[n+1, k+1])}

Crossrefs

Cf. A113287, A113288, A113291 (column 1), A113292 (column 0), A072374.

Sequence in context: A080089 A322841 A291044 * A078442 A175663 A240672

Adjacent sequences: A113287 A113288 A113289 * A113291 A113292 A113293

Keyword

sign,tabl

Author

Paul D. Hanna, Oct 23 2005

Status

approved