A099236 Sums of antidiagonals of A099233.
1, 2, 3, 5, 9, 18, 39, 91, 226, 594, 1643, 4763, 14419, 45444, 148714, 504150, 1766930, 6390720, 23815168, 91306968, 359694457, 1454213026, 6027213531, 25583995337, 111118605583, 493407322280, 2238131105770, 10363617299670, 48954143141361
Offset: 0
Formula
a(n)=sum{j=0..n, sum{k=0..n-j, binomial(j(n-j-k), k)}}