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A099022
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Sum[k=0..n, C(n,k) * (2n-k)! ].
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3
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1, 3, 38, 1158, 65304, 5900520, 780827760, 142358474160, 34209760152960, 10478436416945280, 3984884716852972800, 1842169367191937414400, 1017403495472574045158400, 661599650478455071589606400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Diagonal of Euler-Seidel matrix with start sequence n!.
Number of ways to use the elements of {1,..,k}, n<=k<=2n, once each to form a sequence of n lists, each having length 1 or 2. - Bob Proctor, Apr 18 2005, Jun 26 2006
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LINKS
| Index entries for related partition-counting sequences
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FORMULA
| T(2n, n), where T is the triangle in A076571.
a(n) = 2*n*(2*n-1)*a(n-1)+n*(n-1)*a(n-2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 27 2004
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MATHEMATICA
| Table[(2k)! Hypergeometric1F1[-k, -2k, 1], {k, 0, 10}] (* Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Feb 16 2011 *)
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CROSSREFS
| a(n) = n!*A001517(n).
A082765(n) = Sum[C(n, k)*a(k), 0<=k<=n].
Replace "lists" by "sets" in comment: A105749.
Sequence in context: A109518 A158119 A062155 * A136638 A163789 A183182
Adjacent sequences: A099019 A099020 A099021 * A099023 A099024 A099025
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Sep 23 2004
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