A122177
Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 2, n-k) for n>=k>=0.
Original entry on oeis.org
1, 3, 1, 6, 4, 1, 10, 10, 6, 1, 15, 20, 21, 9, 1, 21, 35, 56, 45, 13, 1, 28, 56, 126, 165, 91, 18, 1, 36, 84, 252, 495, 455, 171, 24, 1, 45, 120, 462, 1287, 1820, 1140, 300, 31, 1, 55, 165, 792, 3003, 6188, 5985, 2600, 496, 39, 1, 66, 220, 1287, 6435, 18564, 26334
Offset: 0
Triangle begins:
1;
3, 1;
6, 4, 1;
10, 10, 6, 1;
15, 20, 21, 9, 1;
21, 35, 56, 45, 13, 1;
28, 56, 126, 165, 91, 18, 1;
36, 84, 252, 495, 455, 171, 24, 1;
45, 120, 462, 1287, 1820, 1140, 300, 31, 1; ...
-
A122177[n_, k_] := Binomial[k*(k + 1)/2 + n - k + 2, n - k];
Table[A122177[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Jul 23 2024 *)
-
T(n,k)=if(n
A121441
Matrix inverse of triangle A121336, where A121336(n,k) = C( n*(n+1)/2 + n-k + 2, n-k) for n>=k>=0.
Original entry on oeis.org
1, -4, 1, 3, -6, 1, -12, 9, -9, 1, -117, -26, 26, -13, 1, -1656, -216, -69, 63, -18, 1, -28506, -3396, -294, -212, 132, -24, 1, -578274, -63116, -5766, -124, -620, 248, -31, 1, -13504179, -1365546, -116116, -8892, 1170, -1612, 429, -39, 1, -356633784, -33696726, -2696316, -186860, -15000, 6228, -3736
Offset: 0
Triangle, A121336^-1, begins:
1;
-4, 1;
3, -6, 1;
-12, 9, -9, 1;
-117, -26, 26, -13, 1;
-1656, -216, -69, 63, -18, 1;
-28506, -3396, -294, -212, 132, -24, 1;
-578274, -63116, -5766, -124, -620, 248, -31, 1;
-13504179, -1365546, -116116, -8892, 1170, -1612, 429, -39, 1; ...
Triangle A121412 begins:
1;
1, 1;
3, 1, 1;
18, 4, 1, 1;
170, 30, 5, 1, 1; ...
Row 3 of A121336^-1 equals row 3 of A121412^(-9), which begins:
1;
-9, 1;
18, -9, 1;
-12, 9, -9, 1; ...
Row 4 of A121336^-1 equals row 4 of A121412^(-13), which begins:
1;
-13, 1;
52, -13, 1;
-52, 39, -13, 1;
-117, -26, 26, -13, 1; ...
-
/* Matrix Inverse of A121336 */ {T(n,k)=local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(r*(r-1)/2+r-c+2,r-c)))); return((M^-1)[n+1,k+1])}
Showing 1-2 of 2 results.
Comments