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EXAMPLE
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1+x = 1 + 1*x/(1+x)^2 + 2*x^2/(1+x)^6 + 9*x^3/(1+x)^12 + 70*x^4/(1+x)^20 + 805*x^5/(1+x)^30 +...
1/(1-x) = 1 + 1*x*(1-x) + 2*x^2*(1-x)^4 + 9*x^3*(1-x)^9 + 70*x^4*(1-x)^16 + 805*x^5*(1-x)^25 +...
Also forms the final terms in rows of the triangle where row n+1 equals the partial sums of row n with the final term repeated 2(n+1) times, starting with a '1' in row 0, as illustrated by:
1;
1, 1;
1, 2, 2, 2, 2;
1, 3, 5, 7, 9, 9, 9, 9, 9, 9;
1, 4, 9, 16, 25, 34, 43, 52, 61, 70, 70, 70, 70, 70, 70, 70, 70;
1, 5, 14, 30, 55, 89, 132, 184, 245, 315, 385, 455, 525, 595, 665, 735, 805, 805, 805, 805, 805, 805, 805, 805, 805, 805;
...
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