Matrix inverse of triangle A122175, where A122175(n,k) = C( k*(k+1)/2 + n-k, n-k) for n>=k>=0.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =1a(4) =-2a(5) =1a(6) =-2a(7) =5a(8) =-4a(9) =1a(10) =7a(11) =-19a(12) =18a(13) =-7a(14) =1a(15) =-37a(16) =104a(17) =-106a(18) =49a(19) =-11a(20) =1a(21) =268a(22) =-766a(23) =809a(24) =-406a(25) =110a(26) =-16a(27) =1a(28) =-2496a(29) =7197