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EXAMPLE
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Let [x^n] F(x) denote the coefficient of x^n in F(x); then
a(0) = 1;
a(1) = [x] (1+x) = 1;
a(2) = [x^2] (1+x)^2*(1+x^2) = 2;
a(3) = [x^3] (1+x)^3*(1+x^2)^2*(1+x^3) = 8;
a(4) = [x^4] (1+x)^4*(1+x^2)^3*(1+x^3)^2*(1+x^4) = 31; ...
as illustrated below.
The coefficients in Product_{k=1..n} (1+x^k)^(n-k+1) for n=0..9 begin:
n=0: [(1), 0, 0, 0, 0, 0, 0, ...];
n=1: [1,(1), 0, 0, 0, 0, 0, 0, 0, 0, ...];
n=2: [1, 2,(2), 2, 1, 0, 0, 0, 0, 0, 0, 0 ...];
n=3: [1, 3, 5, (8), 10, 10, 10, 8, 5, 3, 1, 0 ...];
n=4: [1, 4, 9, 18, (31), 46, 64, 82, 96, 106, 110, 106 ...];
n=5: [1, 5, 14, 33, 68, (124), 210, 332, 492, 693, 931, ...];
n=6: [1, 6, 20, 54, 127, 266, (515), 934, 1597, 2602, ...];
n=7: [1, 7, 27, 82, 215, 502, 1078, (2166), 4109, 7428, ...];
n=8: [1, 8, 35, 118, 340, 870, 2038, 4454, (9182), 18020, ...];
n=9: [1, 9, 44, 163, 511, 1417, 3582, 8420, 18634,(39195), ...]; ...
where the coefficients in parenthesis start this sequence.
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