A172381 Triangle whose inverse has production matrix with general term (-1)^(n-k+1)*C(k+1, n-k+1).

1, 1, 1, 2, 3, 1, 5, 10, 6, 1, 14, 36, 31, 10, 1, 42, 137, 156, 75, 15, 1, 132, 544, 787, 510, 155, 21, 1, 429, 2235, 4017, 3331, 1380, 287, 28, 1, 1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1, 4862, 40876, 109486, 136921, 90665, 33390, 6916, 786, 45, 1, 16796

Offset: 0

Author

Paul Barry, Feb 01 2010

Keywords

• nonn
• tabl

Comments

Product of A033184 and A172380. Diagonal sums are A172382(n+2).

Examples

			Triangle begins
1,
1, 1,
2, 3, 1,
5, 10, 6, 1,
14, 36, 31, 10, 1,
42, 137, 156, 75, 15, 1,
132, 544, 787, 510, 155, 21, 1,
429, 2235, 4017, 3331, 1380, 287, 28, 1,
1430, 9445, 20809, 21405, 11411, 3255, 490, 36, 1,
4862, 40876, 109486, 136921, 90665, 33390, 6916, 786, 45, 1,
16796, 180544, 584955, 877252, 704720, 322728, 86443, 13536, 1200, 55, 1
Production array of inverse is
-1, 1,
0, -2, 1,
0, 1, -3, 1,
0, 0, 3, -4, 1,
0, 0, -1, 6, -5, 1,
0, 0, 0, -4, 10, -6, 1,
0, 0, 0, 1, -10, 15, -7, 1,
0, 0, 0, 0, 5, -20, 21, -8, 1,
0, 0, 0, 0, -1, 15, -35, 28, -9, 1,
0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1,
0, 0, 0, 0, 0, 1, -21, 70, -84, 45, -11, 1