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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 9*x^3 + 60*x^4 + 417*x^5 + 3430*x^6 +...
Form a table of coefficients in A(x)^(2*n) for n>=0, which begins:
[1, 0, 0, 0, 0, 0, 0, 0, 0, ...];
[1, 2, 7, 24, 147, 1008, 8135, 70296, 648172, ...];
[1, 4, 18, 76, 439, 2940, 22936, 194300, 1761411, ...];
[1, 6, 33, 164, 960, 6378, 48526, 403440, 3598050, ...];
[1, 8, 52, 296, 1810, 12128, 90972, 744656, 6542519, ...];
[1, 10, 75, 480, 3105, 21252, 158845, 1286240, 11157705, ...];
[1, 12, 102, 724, 4977, 35100, 263844, 2125020, 18253680, ...];
[1, 14, 133, 1036, 7574, 55342, 421484, 3395016, 28975933, ...];
[1, 16, 168, 1424, 11060, 84000, 651848, 5277696, 44916498, ...]; ...
then the main diagonal forms A005260(n) = Sum_{k=0..n} C(n,k)^4.
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