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

Author

Paul D. Hanna, Oct 06 2013

Keywords

• nonn
• tabl

Examples

			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; ...
		

Crossrefs

Cf. A230050 (row sums), A229711.

Programs

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(""))

Formula

T(n, k) = binomial(k^3+n-k-1, n-k) for n>=k>=0.