|
| |
|
|
A033030
|
|
Derangement numbers d(n,3) where d(n,k) = k(n-1)(d(n-1,k) + d(n-2,k)), with d(0,k) = 1 and d(1,k) = 0.
|
|
4
| |
|
|
1, 0, 3, 18, 189, 2484, 40095, 766422, 16936857, 424878696, 11929019931, 370616958810, 12624017298453, 467806833261468, 18736803171836919, 806593620214132254, 37139869052368612785, 1821430208283971761872, 94787073944153359107507, 5216859224231615866946466
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
FORMULA
| Inverse binomial transform of A007559. E.g.f.: exp(-x)/(1-3*x)^(1/3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 17 2003
a(n) = 3(n-1)(a(n-1)+a(n-2)), n>1 [From Gary Detlefs (gdetlefs(AT)aol.com), May 16 2010]
|
|
|
EXAMPLE
| 3= 3*(1+0), 18 =6*(0+3), 189=9*(18+3), 2484=12*(189+18)... [From Gary Detlefs (gdetlefs(AT)aol.com), May 16 2010]
|
|
|
MAPLE
| k := 3; d := proc(n) global k; option remember; if n = 0 then RETURN(1) end if; if n = 1 then RETURN(0) end if; k*(n - 1)*(d(n - 1) + d(n - 2)) end proc;
|
|
|
CROSSREFS
| d(n, 1) gives A000166, d(n, 2) gives A053871, d(n, 4) gives A088991, d(n, 5) gives A088992.
Sequence in context: A132853 A084879 A141118 * A178014 A002824 A160707
Adjacent sequences: A033027 A033028 A033029 * A033031 A033032 A033033
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2003
|
| |
|
|
