|
| |
|
|
A055140
|
|
Triangle: matchings of 2n people with partners (of either sex) such that exactly k couples are left together.
|
|
2
|
|
|
|
1, 0, 1, 2, 0, 1, 8, 6, 0, 1, 60, 32, 12, 0, 1, 544, 300, 80, 20, 0, 1, 6040, 3264, 900, 160, 30, 0, 1, 79008, 42280, 11424, 2100, 280, 42, 0, 1, 1190672, 632064, 169120, 30464, 4200, 448, 56, 0, 1, 20314880, 10716048, 2844288, 507360, 68544, 7560, 672, 72, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
T is an example of the group of matrices outlined in the table in A132382--the associated matrix for aC(1,1). The e.g.f. for the row polynomials is exp(x*t) * exp(-x) * (1-2*x)^(-1/2). T(n,k) = Binomial(n,k)* s(n-k) where s = A053871 with an e.g.f. of exp(-x) * (1-2*x)^(-1/2) which is the reciprocal of the e.g.f. of A055142. The row polynomials form an Appell sequence. [From Tom Copeland, Sep 10 2008]
|
|
|
LINKS
|
Table of n, a(n) for n=0..53.
|
|
|
FORMULA
|
a(n, k) = A053871(n-k)*C(n, k).
|
|
|
EXAMPLE
|
1; 0,1; 2,0,1; 8,6,0,1; 60,32,12,0,1; ...
|
|
|
MAPLE
|
g[0] := 1: g[1] := 0: for n from 2 to 20 do g[n] := (2*(n-1))*(g[n-1]+g[n-2]) end do: T := proc (n, k) options operator, arrow; g[n-k]*binomial(n, k) end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form [From Emeric Deutsch, Jan 24 2009]
|
|
|
CROSSREFS
|
Cf. A055141, A055142.
Sequence in context: A108998 A201637 A055141 * A191936 A021836 A072551
Adjacent sequences: A055137 A055138 A055139 * A055141 A055142 A055143
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Christian G. Bower, May 09 2000
|
|
|
STATUS
|
approved
|
| |
|
|
