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A230049
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Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.
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2
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1, 0, 1, 0, 1, 1, 0, 1, 8, 1, 0, 1, 36, 27, 1, 0, 1, 120, 378, 64, 1, 0, 1, 330, 3654, 2080, 125, 1, 0, 1, 792, 27405, 45760, 7875, 216, 1, 0, 1, 1716, 169911, 766480, 333375, 23436, 343, 1, 0, 1, 3432, 906192, 10424128, 10668000, 1703016, 58996, 512, 1, 0, 1, 6435, 4272048, 119877472, 275234400, 93240126, 6784540, 131328, 729, 1
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OFFSET
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0,9
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LINKS
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FORMULA
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T(n, k) = binomial(k^3+n-k-1, n-k) for n>=k>=0.
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 8, 1;
0, 1, 36, 27, 1;
0, 1, 120, 378, 64, 1;
0, 1, 330, 3654, 2080, 125, 1;
0, 1, 792, 27405, 45760, 7875, 216, 1;
0, 1, 1716, 169911, 766480, 333375, 23436, 343, 1;
0, 1, 3432, 906192, 10424128, 10668000, 1703016, 58996, 512, 1;
0, 1, 6435, 4272048, 119877472, 275234400, 93240126, 6784540, 131328, 729, 1; ...
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PROG
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(PARI) {T(n, k) = polcoeff(1/(1-x+x*O(x^n))^(k^3), n-k)}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))
(PARI) {T(n, k) = binomial(k^3+n-k-1, n-k)}
for(n=0, 12, 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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