Let r = 100001.00000000009999800002999940001499964000... (the real root of x^3-100001*x^2-1). Now we print the powers of r with underscores for zeros to make the pattern apparent: [ 0, 1] [ 1, 1____1.__________99998____299994___1499964___8399796__512987___3311] [ 2, 1____2____1.____199998____199995___1399968___7199823__44998864_2882] [ 3, 1____3____3____3.999999999999997____899982___3999895__27299314_1746] [ 4, 1____4____6____8____4.9999999998____399994___159995___13199671__856] [ 5, 1____5___10___15___15____6.___________________49998____4999875__35_] [ 6, 1____6___15___26___33___24___10.______________199994___1199965__12_] [ 7, 1____7___21___42___63___63___42___14.9999999999999999999999993___35] [ 8, 1____8___28___64__110__136__120___72___20.99999999999999999998____8] [ 9, 1____9___36___93__180__261__282__225__117___31.____________________] [10, 1___10___45__130__280__462__585__570__405__190___46._______________] [11, 1___11___55__176__418__770_1111_1265_1111__715__308___67.__________] [12, 1___12___66__232__603_1224_1974_2556_2637_2108_1248__492___98._____] [13, 1___13___78__299__845_1872_3328_4810_5655_5330_3926_2145__780__144 E65] The diagonal seq. appears to be http://oeis.org/A001609 What could the triangle be (if the polynomial is replaced by x^3-(10^k+1)*x^2-1 for large k)? And: do I get a cookie?