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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS 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: A209914 A342980 A094922 * A088990 A214097 A194732 Adjacent sequences:  A230046 A230047 A230048 * A230050 A230051 A230052 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Oct 06 2013 STATUS approved

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Last modified January 20 18:38 EST 2022. Contains 350472 sequences. (Running on oeis4.)