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EXAMPLE
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Ignoring the initial term, this sequence forms the logarithmic series:
L(x) = 2*x + 18*x^2/2 + 560*x^3/3 + 68614*x^4/4 + 34210752*x^5/5 + ...
exp(L(x)) = 1 + 2*x + 11*x^2 + 206*x^3 + 17586*x^4 + 6878604*x^5 + ...
Illustrate definition.
The coefficients of x^k in (1 + 2^n*x + x^2)^n, k=0..2n, n>=0, begin:
n=0: [(1)];
n=1: [1, (2), 1];
n=2: [1, 8, (18), 8, 1];
n=3: [1, 24, 195, (560), 195, 24, 1];
n=4: [1, 64, 1540, 16576, (68614), 16576, 1540, 64, 1];
n=5: [1, 160, 10245, 328320, 5273610, (34210752), 5273610, 328320, ...];
n=6: [1, 384, 61446, 5244800, 251904015, 6458183424, (69223161876), ...];
n=7: [1, 896, 344071, 73405696, 9396961301, 721848120448, 30814514741283, (564393502852608), ...]; ...
where the above central coefficients in parenthesis form this sequence.
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