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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 A094965

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 September 20 09:28 EDT 2021. Contains 347579 sequences. (Running on oeis4.)