a(n,m) tabl head (triangle) for A129062 Matrix product S2*|S1|, i.e. a(n,m)==sum(S2(n,k)*|S1(k,m)|,k=m..n), n>=0. n\m 0 1 2 3 4 5 6 7 8 9 ... 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 0 2 1 0 0 0 0 0 0 0 3 0 6 6 1 0 0 0 0 0 0 4 0 26 36 12 1 0 0 0 0 0 5 0 150 250 120 20 1 0 0 0 0 6 0 1082 2040 1230 300 30 1 0 0 0 7 0 9366 19334 13650 4270 630 42 1 0 0 8 0 94586 209580 166376 62160 11900 1176 56 1 0 9 0 1091670 2562354 2229444 952728 220500 28476 2016 72 1 . . . E.g.f. column nr. m (leading zeros): ((-ln(2-exp(x))^m)/m!, m>=0. Due to Jabotinsky structure: S2 has e.g.f. for second (m=1) column exp(x)-1, |S1| has e.g.f. for second column -ln(1-x). Therefore the product S2*|S1| has e.g.f. for the second column -ln(1-(exp(x)-1)) = -ln(2-exp(x)). From the e.g.f.s for the columns one gets the e.g.f. for the row polynomials P(n,x):=sum(a(n,m)*x^m,m=0..n) as 1/(2-exp(z))^x. E.g.f. row sums 1/(2-exp(x)): A000670 [1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, ...]. Columns without leading zeros: m=1: A000629, m=2: A129063, m=3: A129064. ######################################### e.o.f. ###############################################