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A076015
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Sum of the (n-1)-th powers of the first n integers.
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9
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1, 3, 14, 100, 979, 12201, 184820, 3297456, 67731333, 1574304985, 40851766526, 1170684360924, 36720042483591, 1251308658130545, 46034015337733480, 1818399978159990976, 76762718946972480009
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OFFSET
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1,2
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COMMENTS
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a(n) is the number of length n sequences of [n] that start with their maximum value.
By symmetry, counts many other simple classes of endofunctions.
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LINKS
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FORMULA
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a(n) = Sum_{m=1..n} m^(n-1), n >= 1.
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EXAMPLE
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The 3 sequences for n=2 are 11, 21, 22.
The 14 = 3^0 + 3^1 + 3^2 sequences starting with their maximum value for n=3 are 111, 211, 212, 221, 222, 311, 312, 313, 321, 322, 323, 331, 332, 333.
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MAPLE
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a:=n->sum((n-j+1)^n, j=0..n): seq(a(n), n=0..17); # Zerinvary Lajos, Jun 05 2008
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MATHEMATICA
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Table[Sum[m^(n-1), {m, n}], {n, 20}] (* Harvey P. Dale, Jan 26 2016 *)
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PROG
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(PARI) vector(20, n, sum(m=1, n, m^(n-1))) \\ Michel Marcus, Jan 14 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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