A110554 Column 11 of table A105552.
56, 285, 954, 2366, 4711, 7936, 11712, 15448, 18450, 20155, 20329, 19078, 16746, 13780, 10644, 7712, 5235, 3325, 1970, 1081, 544, 247, 99, 33, 8, 1
Offset: 1
Examples
a(6) = A107601(6) = 7936.
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a(6) = A107601(6) = 7936.
a(3) = 14, because there are 14 ordered 3-tuples of positive integers such that the largest value is 3 and the first value is odd: 113, 123, 131, 132, 133, 311, 312, 313, 321, 322, 323, 331, 332, 333.
a:= n-> (Matrix (`if` (irem(n, 2)=0, [n/2, 0], [1 +(n-1)/2*3, 1])). Matrix ([[2*n-1, 1], [n*(1-n), 0]]) ^(n-1))[1, 2]: seq (a(n), n=1..20);
a(0) = 1: (). a(1) = 1: (a). a(2) = 1: (b,b). a(3) = 5: (a,c,a), (b,c,b), (c,a,c), (c,b,c), (c,c,c).
a:= n-> (h-> n^h-`if`(n=0, 0, (n-1)^h))(ceil(n/2)): seq(a(n), n=0..25); # Alois P. Heinz, Nov 21 2024
h[n_] := Ceiling[n/2];a[n_] := n^h[n] - (n - 1)^h[n];Join[{1},Table[a[n],{n,25}]] (* James C. McMahon, Nov 21 2024 *)
h(n) = {ceil(n/2)}
a(n) = {n^h(n)-(n-1)^h(n)}
def A378203(n): return n**(m:=n+1>>1)-(n-1)**m if n else 1 # Chai Wah Wu, Nov 21 2024
The table begins 1 1 1 1 3 1 1 7 4 2 1 15 12 10 5 1 31 32 36 30 14 the third diagonal is 1 4 12 32 80 192 448 ... A001787 which, in turn, is the row sum of the below table 1 2 2 3 6 3 4 12 12 4 5 20 30 20 5 which counts the permutations of 3; 32, 31; 322, 321, 311; 3222, 3221, 3211, 3111; etc.
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