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A249677
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Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^3*x).
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4
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1, 1, 1, 1, 9, 8, 1, 36, 251, 216, 1, 100, 2555, 16280, 13824, 1, 225, 15055, 335655, 2048824, 1728000, 1, 441, 63655, 3587535, 74550304, 444273984, 373248000, 1, 784, 214918, 25421200, 1305074809, 26015028256, 152759224512, 128024064000, 1, 1296, 616326, 135459216, 14320729209, 694213330464, 13472453691584, 78340747014144, 65548320768000
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OFFSET
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0,5
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COMMENTS
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Column 1 forms the squares of the triangular numbers (A000537).
Main diagonal forms the cubes of the factorial numbers (A000442).
Row sums equal Product_{k=1..n} (k^3 + 1) = n!*Product_{k=1..n} (k*(k-1) + 1) = n!*A130032(n).
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 9, 8;
1, 36, 251, 216;
1, 100, 2555, 16280, 13824;
1, 225, 15055, 335655, 2048824, 1728000;
1, 441, 63655, 3587535, 74550304, 444273984, 373248000;
1, 784, 214918, 25421200, 1305074809, 26015028256, 152759224512, 128024064000;
1, 1296, 616326, 135459216, 14320729209, 694213330464, 13472453691584, 78340747014144, 65548320768000; ...
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PROG
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(PARI) {T(n, k)=polcoeff(prod(m=0, n, 1 + m^3*x +x*O(x^n)), k)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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