 | ECS #261: Binomial coefficients |
| Introduction | Examples | Search | Submit | Help | Links |
1. Description
Arrangements of n unlabelled objects in 12 rows
2. Specification
This unlabelled structure is specified as S in
\displaystyle
\left\{ B={\rm Sequence} \left( Z \right) ,S={\rm Prod} \left( B,B,B,B
,B,B,B,B,B,B,B,B \right) \right\}
other formats
3. Coefficients
3.1. First terms
3.2. Recurrence
\displaystyle
\left\{ 39916800\,f \left( n \right) -{n}^{11}-66\,{n}^{10}-1925\,{n}^
{9}-32670\,{n}^{8}-357423\,{n}^{7}-2637558\,{n}^{6}-13339535\,{n}^{5}-
45995730\,{n}^{4}-105258076\,{n}^{3}-150917976\,{n}^{2}-120543840\,n-
39916800=0,f \left( 0 \right) =1 \right\}
other formats
3.3. Closed form
\displaystyle
{\frac {1}{39916800}}\, \left( n+1 \right) \left( n+2 \right) \left(
n+3 \right) \left( n+4 \right) \left( n+5 \right) \left( n+6
\right) \left( n+7 \right) \left( n+8 \right) \left( n+9 \right)
\left( n+10 \right) \left( n+11 \right)
other formats
3.4. Asymptotics
4. Ordinary generating function
\displaystyle
\left( -1+x \right) ^{-12}
other formats
5. References
6. Random structure
Search a combinatorial structure by: (firstTerms should be a sequence of integers, separated by commas).