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Search: id:A055140
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| A055140 |
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Triangle: matchings of 2n people with partners (of either sex) such that exactly k couples are left together. |
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3
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| 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; listen)
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OFFSET
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0,4
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COMMENT
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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 (tcjpn(AT)msn.com), Sep 10 2008]
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FORMULA
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a(n, k) = A053871(n-k)*C(n, k).
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EXAMPLE
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1; 0,1; 2,0,1; 8,6,0,1; 60,32,12,0,1; ...
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MAPLE
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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 (deutsch(AT)duke.poly.edu), Jan 24 2009]
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CROSSREFS
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Cf. A055141, A055142.
Sequence in context: A065329 A108998 A055141 this_sequence A021836 A072551 A091803
Adjacent sequences: A055137 A055138 A055139 this_sequence A055141 A055142 A055143
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), May 09 2000
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