A125278 Convolution triangle of A030266, which shifts left under self-COMPOSE.
1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 23, 16, 9, 4, 1, 104, 62, 31, 14, 5, 1, 531, 278, 123, 52, 20, 6, 1, 2982, 1398, 552, 213, 80, 27, 7, 1, 18109, 7718, 2750, 964, 340, 116, 35, 8, 1, 117545, 46083, 14976, 4784, 1561, 513, 161, 44, 9, 1, 808764, 294392, 88083, 25792, 7755
Offset: 0
Examples
Triangle begins: 1; 1, 1; 2, 2, 1; 6, 5, 3, 1; 23, 16, 9, 4, 1; 104, 62, 31, 14, 5, 1; 531, 278, 123, 52, 20, 6, 1; 2982, 1398, 552, 213, 80, 27, 7, 1; 18109, 7718, 2750, 964, 340, 116, 35, 8, 1; 117545, 46083, 14976, 4784, 1561, 513, 161, 44, 9, 1; 808764, 294392, 88083, 25792, 7755, 2400, 742, 216, 54, 10, 1; ... Matrix square T^2 begins: 1; 2, 1; 6, 4, 1; 23, 16, 6, 1; 104, 70, 30, 8, 1; 531, 336, 149, 48, 10, 1; ... which is also a convolution triangle.
Programs
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PARI
T(n,k)=if(n
0,sum(j=0,n-k,T(j,0)*T(n-1-j,k-1)), sum(j=0,n-1,T(j,0)*T(n-1,j)))))
Comments