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EXAMPLE
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The coefficients in Product_{k=0..n-1} (1+k*x+x^2) form triangle A201949:
(1);
1,(0), 1;
1, 1,(2), 1, 1;
1, 3, 5, (6), 5, 3, 1;
1, 6, 15, 24, (28), 24, 15, 6, 1;
1, 10, 40, 90, 139, (160), 139, 90, 40, 10, 1;
1, 15, 91, 300, 629, 945, (1078), 945, 629, 300, 91, 15, 1;
1, 21, 182, 861, 2520, 5019, 7377, (8358), 7377, 5019, 2520, 861, 182, 21, 1;
1, 28, 330, 2156, 8729, 23520, 45030, 65016, (73260), 65016, 45030, 23520, 8729, 2156, 330, 28, 1; ...
where coefficients in parenthesis form the initial terms of this sequence.
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PROG
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(PARI) {a(n) = polcoeff( prod(k=1, n, 1+(k-1)*x+x^2+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))
{a(n) = n!*polcoeff( sum(m=0, n, log(1 - x +x*O(x^n))^(2*m)/m!^2), n)}
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