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 A219570 Triangular array read by rows. T(n,k) is the number of necklaces (turning over is not allowed) of n labeled black or white beads having exactly k black beads. 2
 0, 1, 1, 1, 2, 1, 2, 6, 6, 2, 6, 24, 36, 24, 6, 24, 120, 240, 240, 120, 24, 120, 720, 1800, 2400, 1800, 720, 120, 720, 5040, 15120, 25200, 25200, 15120, 5040, 720, 5040, 40320, 141120, 282240, 352800, 282240, 141120, 40320, 5040, 40320, 362880, 1451520, 3386880, 5080320, 5080320, 3386880, 1451520, 362880, 40320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A066318. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1274 FORMULA E.g.f.: log(1/(1 - (y + 1)*x)). T(n, k) = (n-1)! * binomial(n, k) for n > 0. - Andrew Howroyd, Oct 11 2017 EXAMPLE 0; 1, 1; 1, 2, 1; 2, 6, 6, 2; 6, 24, 36, 24, 6; 24, 120, 240, 240, 120, 24; 120, 720, 1800, 2400, 1800, 720, 120; 720, 5040, 15120, 25200, 25200, 15120, 5040, 720; MATHEMATICA nn=8; f[list_]:=Select[list, #>0&]; Map[f, Drop[Range[0, nn]!CoefficientList[Series[Log[1/(1-(y+1)x)], {x, 0, nn}], {x, y}], 1]]//Grid PROG (PARI) T(n, k) = if(n>0, (n-1)! * binomial(n, k)); \\ Andrew Howroyd, Oct 11 2017 CROSSREFS Sequence in context: A301361 A267864 A336524 * A285030 A281781 A351317 Adjacent sequences: A219567 A219568 A219569 * A219571 A219572 A219573 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Nov 23 2012 STATUS approved

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Last modified August 14 05:41 EDT 2024. Contains 375146 sequences. (Running on oeis4.)