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A230049
Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.
2
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
OFFSET
0,9
FORMULA
T(n, k) = binomial(k^3+n-k-1, n-k) for n>=k>=0.
EXAMPLE
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; ...
PROG
(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(""))
CROSSREFS
Cf. A230050 (row sums), A229711.
Sequence in context: A365237 A342980 A094922 * A088990 A351129 A214097
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Oct 06 2013
STATUS
approved