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A174552 Triangular array T(n,k): The differences in the columns of A174551. 0
1, 0, 1, 1, 1, 2, 8, 7, 6, 6, 81, 65, 50, 36, 24, 1024, 781, 570, 390, 240, 120, 15625, 11529, 8162, 5460, 3360, 1800, 720, 279936, 201811, 140070, 92526, 57120, 31920, 15120, 5040 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the image of f contains {1,2,...,k} but not k+1.
Row sums = n^n.
Columns are asymptotic to n^n (1/e)(1-(1/e))^k.
Sum k*T(n,k) appears to be A055869.
LINKS
EXAMPLE
Triangle begins:
1;
0, 1;
1, 1, 2;
8, 7, 6, 6;
81,65,50,36,24;
1024,781,570,390,240,120;
15625, 11529, 8162, 5460, 3360, 1800, 720...
MATHEMATICA
Table[Append[(-1) Differences[ Table[Sum[(-1)^i Binomial[k, i] (n - i)^n, {i, 0, k}], {k, 0, n}]], n! ], {n, 0, 7}] // Grid
CROSSREFS
Sequence in context: A268308 A027606 A202693 * A083679 A213930 A319463
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 22 2010
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)