A113290
Matrix logarithm of triangle A113287.
Original entry on oeis.org
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
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; ...
-
{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
A113288
Matrix inverse of triangle A113287.
Original entry on oeis.org
1, -2, 1, 3, 0, 1, -8, -4, -4, 1, 15, 10, 10, 0, 1, -36, -30, -36, -12, -6, 1, 77, 70, 91, 42, 21, 0, 1, -192, -184, -256, -152, -96, -24, -8, 1, 459, 450, 648, 432, 306, 108, 36, 0, 1, -1220, -1210, -1780, -1280, -1000, -460, -200, -40, -10, 1, 3201, 3190, 4741, 3542, 2926, 1540, 770, 220, 55, 0, 1
Offset: 0
Triangle begins:
.1;
.-2,1;
.3,0,1;
.-8,-4,-4,1;
.15,10,10,0,1;
.-36,-30,-36,-12,-6,1;
.77,70,91,42,21,0,1;
.-192,-184,-256,-152,-96,-24,-8,1;
.459,450,648,432,306,108,36,0,1;
.-1220,-1210,-1780,-1280,-1000,-460,-200,-40,-10,1;
.3201,3190,4741,3542,2926,1540,770,220,55,0,1; ...
-
{T(n,k)=local(x=X+O(X^(n+2)),y=Y+O(Y^(n+2)),M=matrix(n+1,n+1,r,c, polcoeff(polcoeff(1/(1-x*y)+r*x/((1-x*y)*(1+x+x*y)),r-1,X),c-1,Y))); if(n
A113291
a(n) = A113290(n,1)/(n+1) for n>=0, where A113290 is the matrix log of triangle A113287.
Original entry on oeis.org
0, 0, 0, 1, -2, 4, -7, 13, -24, 48, -99, 221, -512, 1268, -3247, 8773, -24400, 70896, -211347, 653541, -2068472, 6755684, -22541135, 77305981, -270435640, 969413776, -3539893923, 13212871629, -50180362320, 194412817844, -765590169935, 3070433223317
Offset: 0
-
a(n)=if(n<3,0,(-1)^(n-3)*sum(k=0,n-3,sum(j=0,k\2,(k-j)!/(k-2*j)!)))
A113292
Column 0 of triangle A113290, which is the matrix log of A113287.
Original entry on oeis.org
0, 2, -3, 6, -10, 19, -35, 72, -150, 343, -803, 2024, -5226, 14299, -40027, 117392, -351798, 1095735, -3483403, 11442896, -38326586, 132070827, -463565299, 1668391912, -6110374070, 22885849335, -87147853011, 338645273368, -1336767522026, 5375276276699
Offset: 0
Original entry on oeis.org
1, -1, 4, -15, 36, -119, 302, -911, 2440, -7199, 20186, -60359, 177204, -546615, 1683286, -5401759, 17456128, -58447151, 197925490, -691264279, 2446636396, -8897012871, 32811147054, -123933345455, 474792813176, -1858243857599, 7375013350282, -29840434526951
Offset: 0
Showing 1-5 of 5 results.