A073151 Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n+1,0)=A006319(n)=a(n,0) + Sum a(k,k), k=0..n-1. a(n,m+1)= a(n,0) + Sum A006319(k)*a(n-k-1,0), k=0..m-1.
1, 1, 2, 4, 5, 9, 16, 20, 24, 40, 68, 84, 100, 116, 184, 304, 372, 436, 500, 568, 872, 1412, 1716, 1988, 2244, 2516, 2820, 4232, 6752, 8164, 9380, 10468, 11556, 12772, 14184, 20936, 33028
Offset: 0
Examples
a(4,2)=a(4,0)+1*a(3,0)+4*a(2,0)=68+(1*16+4*4)=100. a(4,0)=a(3,0)+a(3,3)+a(2,2)+a(1,1)+a(0,0)=16+(40+9+2+1)=68. Rows of triangle: {1}, {1,2}, {4,5,9}, {16,20,24,40}, {68,84,100,116,184},{304,372,436,500,568,872}, {1412,1716,1988,2244,2516,2820,4232}, ...
Formula
a(n, m+1) = a(n, 0) + Sum A006319(k)*a(n-k-1, 0), k=0..m-1.
Comments