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.

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

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