A155194 Triangle read by rows: t(n,m)=If[m*(n - m) == 0, 1, n!*(1 - 1/Binomial[n, m])].

1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 18, 20, 18, 1, 1, 96, 108, 108, 96, 1, 1, 600, 672, 684, 672, 600, 1, 1, 4320, 4800, 4896, 4896, 4800, 4320, 1, 1, 35280, 38880, 39600, 39744, 39600, 38880, 35280, 1, 1, 322560, 352800, 358560, 360000, 360000, 358560, 352800

Offset

0,8

Comments

Row sums are {1, 2, 3, 10, 58, 410, 3230, 28034, 267266, 2787842, 31662722,...}

Links

Table of n, a(n) for n=0..52.

Example

{1},
{1, 1},
{1, 1, 1},
{1, 4, 4, 1},
{1, 18, 20, 18, 1},
{1, 96, 108, 108, 96, 1},
{1, 600, 672, 684, 672, 600, 1},
{1, 4320, 4800, 4896, 4896, 4800, 4320, 1},
{1, 35280, 38880, 39600, 39744, 39600, 38880, 35280, 1},
{1, 322560, 352800, 358560, 360000, 360000, 358560, 352800, 322560, 1},
{1, 3265920, 3548160, 3598560, 3611520, 3614400, 3611520, 3598560, 3548160, 3265920, 1}

Mathematica

Table[Table[ If[m*(n - m) == 0, 1, n!*(1 - 1/Binomial[n, m])], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A075613 A221837 A189150 * A080044 A128433 A089746

Adjacent sequences: A155191 A155192 A155193 * A155195 A155196 A155197

Keyword

nonn,tabl

Author

Roger L. Bagula, Jan 21 2009

Extensions

Edited by N. J. A. Sloane, Jan 25 2009

Status

approved