A230049 Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.

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

Links

Table of n, a(n) for n=0..65.

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

Adjacent sequences: A230046 A230047 A230048 * A230050 A230051 A230052

Keyword

nonn,tabl

Author

Paul D. Hanna, Oct 06 2013

Status

approved