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 A221833 Triangle, read by rows, where T(n,k) = [x^n] x^k*(1-x^k)^(k-1) / (1-x)^(k-1) for n>=k>=1. 1
 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 3, 3, 1, 0, 0, 2, 6, 4, 1, 0, 0, 1, 10, 10, 5, 1, 0, 0, 0, 12, 20, 15, 6, 1, 0, 0, 0, 12, 35, 35, 21, 7, 1, 0, 0, 0, 10, 52, 70, 56, 28, 8, 1, 0, 0, 0, 6, 68, 126, 126, 84, 36, 9, 1, 0, 0, 0, 3, 80, 205, 252, 210, 120, 45, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS FORMULA G.f. of column k = x^k * ( (1-x^k)/(1-x) )^(k-1). EXAMPLE Triangle begins: 1; 0, 1; 0, 1, 1; 0, 0, 2, 1; 0, 0, 3, 3, 1; 0, 0, 2, 6, 4, 1; 0, 0, 1, 10, 10, 5, 1; 0, 0, 0, 12, 20, 15, 6, 1; 0, 0, 0, 12, 35, 35, 21, 7, 1; 0, 0, 0, 10, 52, 70, 56, 28, 8, 1; 0, 0, 0, 6, 68, 126, 126, 84, 36, 9, 1; 0, 0, 0, 3, 80, 205, 252, 210, 120, 45, 10, 1; 0, 0, 0, 1, 85, 305, 462, 462, 330, 165, 55, 11, 1; 0, 0, 0, 0, 80, 420, 786, 924, 792, 495, 220, 66, 12, 1; ... in which column sums equal: A000169(k) = k^(k-1) for k>=1. PROG (PARI) {T(n, k)=polcoeff(((1-x^k)/(1-x +x*O(x^n)))^(k-1), n-k)} for(n=1, 12, for(k=1, n, print1(T(n, k), ", ")); print("")) CROSSREFS Cf. A221834, A000169, A077227. Sequence in context: A055334 A106237 A071675 * A319082 A034365 A103778 Adjacent sequences:  A221830 A221831 A221832 * A221834 A221835 A221836 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jan 26 2013 STATUS approved

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Last modified January 29 01:54 EST 2020. Contains 331328 sequences. (Running on oeis4.)