|
| |
|
|
A115112
|
|
Number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set.
|
|
3
| |
|
|
0, 4, 18, 68, 250, 922, 3430, 12868, 48618, 184754, 705430, 2704154, 10400598, 40116598, 155117518, 601080388, 2333606218, 9075135298, 35345263798, 137846528818, 538257874438, 2104098963718, 8233430727598, 32247603683098
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set.
|
|
|
LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
|
|
|
FORMULA
| a(n) = binomial(2*n, n)-2; also: a(n)=sum{binomial(n, i)*binomial(n, j|i, j=1...(n-1), i+j=n}.
|
|
|
EXAMPLE
| a(5)=binomial(10,5)-2=250.
|
|
|
MAPLE
| seq(sum((binomial(n, m))^2, m=1..n-1), n=1..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
|
|
|
MATHEMATICA
| Table[Sum[Binomial[n, i] Binomial[n, n - i], {i, 1, n - 1}], {n, 0,
10}]
|
|
|
CROSSREFS
| Cf. A000984, A115246, A115111.
Sequence in context: A083321 A022728 * A171074 A005367 A050184 A034352
Adjacent sequences: A115109 A115110 A115111 * A115113 A115114 A115115
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 22 2006
|
| |
|
|
