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A055869
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a(n) = (n+1)^n - n^n.
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9
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1, 5, 37, 369, 4651, 70993, 1273609, 26269505, 612579511, 15937424601, 457696700077, 14381984674225, 490839666661891, 18080919199832609, 715027614225987601, 30214447801957316865, 1358671297852359767791, 64780942222614703957417, 3264460344339686410876021
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OFFSET
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1,2
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COMMENTS
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Number of functions f:[n]->[n+1] such that some x in [n] maps to n+1.
Number of switching generators for a power polyadic n-context ({1..k}, ..., {1..k}, <>) with n=k [Theorems 5 and 6, page 81, in Ignatov]. - Dmitry I. Ignatov, Nov 23 2022
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LINKS
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FORMULA
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E.g.f.: W(-x)*(x-1)/((1+W(-x))*x), W(x) principal branch of Lambert's function.
With interpolated zeros, ceiling(n/2)^floor(n/2) - floor(n/2)^floor(n/2). - Paul Barry, Jul 13 2005
a(n) = Sum_{k=1..n} (-1)^(n-k)*k!*Stirling2(n,k)*binomial(n+k-1,n). - Vladimir Kruchinin, Sep 20 2015
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MATHEMATICA
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PROG
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(PARI) vector(20, n, (n+1)^n - n^n) \\ Michel Marcus, Jan 10 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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