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 A133721 Triangle read by rows: T(m,n) = number of n-balanced and minimal labeled covers of a finite set of m unlabeled elements (m >= 1, 1 <= n <= m). 5
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 7, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 10, 1, 13, 1, 1, 1, 1, 1, 1, 1, 25, 7, 1, 1, 1, 1, 1, 1, 1, 15, 6, 3, 22, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 21, 65, 81, 7, 34, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 LINKS Table of n, a(n) for n=1..94. A. P. Burger and J. H. van Vuuren, Balanced minimal covers of a finite set, Discr. Math. 307 (2007), 2853-2860. EXAMPLE Triangle begins: 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 6 7 1 1 1 1 1 1 3 1 1 1 1 1 1 10 1 13 1 1 1 1 1 1 1 25 7 1 1 1 1 1 1 1 15 6 3 22 1 1 1 1 1 1 MAPLE A133721 := proc(m, n) l := ceil(m/n) ; c := n*ceil(m/n)-m ; A133713(l, c) ; end proc: # R. J. Mathar, Nov 23 2011 MATHEMATICA A133713[l_, cl_] := Module[{g, k, s}, g = 1; For[k = 1, k <= cl+1, k++, s = Sum[Binomial[Binomial[l, k+1] + i-1, i]*t^(i*k), {i, 0, Ceiling[cl/k]}]; g = g*s]; g = Expand[g]; SeriesCoefficient[g, {t, 0, cl}]]; A133713[_, 0] = 1; a[m_, n_] := A133713[Ceiling[m/n], n*Ceiling[m/n] - m]; Table[a[m, n], {m, 1, 14}, {n, 1, m}] // Flatten (* Jean-François Alcover, Jan 20 2014, after R. J. Mathar *) CROSSREFS Cf. A133709. Column n=2 is essentially A000217. Columns 3, 4, 5, 6 give A133722, A133723, A133724, A133733. Sequence in context: A368711 A049586 A342466 * A083202 A030560 A030559 Adjacent sequences: A133718 A133719 A133720 * A133722 A133723 A133724 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Dec 30 2007 STATUS approved

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Last modified March 2 04:55 EST 2024. Contains 370460 sequences. (Running on oeis4.)