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A097967
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Sum_{k=1..n} (P(n,k) + C(n,k)).
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0
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0, 2, 7, 22, 79, 356, 2019, 13826, 109855, 986920, 9865123, 108507158, 1302065439, 16926805676, 236975181187, 3554627504842, 56874039618751, 966858672535760, 17403456103546563, 330665665962928286, 6613313319249128575
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{k=1..n} n!(k!+1) / k!(n-k)! = Sum_{k=1..n} P(n, k)+2^n-1 = A007526(n) - A000225(n) - 1 = A097656(n) - 2.
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EXAMPLE
| a(2) = 7 because P(2,1) = 2, P(2,2) = 2 while C(2,1)= 2, C(2,2) = 1 and 2 + 2 + 2 + 1 = 7.
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MATHEMATICA
| f[n_] := Sum[n!(k! + 1)/(k!(n - k)!), {k, n}]; Table[ f[n], {n, 0, 20}] (from Robert G. Wilson v Sep 24 2004)
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CROSSREFS
| Cf. A097656, A007526, A000225.
Sequence in context: A132838 A047095 A110137 * A052879 A007867 A014558
Adjacent sequences: A097964 A097965 A097966 * A097968 A097969 A097970
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KEYWORD
| nonn
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Sep 21 2004
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 24 2004
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