OFFSET
0,5
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
FORMULA
Sum_{k=1..n} k * T(n,k) = A327548(n).
EXAMPLE
T(3,1) = 4: 3, 21, 12, 111.
T(3,2) = 2: 2|1, 11|1.
T(3,3) = 1: 1|1|1.
Triangle T(n,k) begins:
1;
0, 1;
0, 2, 1;
0, 4, 2, 1;
0, 8, 8, 2, 1;
0, 16, 16, 8, 2, 1;
0, 32, 48, 24, 8, 2, 1;
0, 64, 96, 64, 24, 8, 2, 1;
0, 128, 256, 160, 80, 24, 8, 2, 1;
0, 256, 512, 448, 192, 80, 24, 8, 2, 1;
0, 512, 1280, 1024, 576, 224, 80, 24, 8, 2, 1;
...
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+expand(2^(i-1)*x*b(n-i, min(n-i, i)))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)):
seq(T(n), n=0..12);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + 2^(i-1) x b[n-i, Min[n-i, i]]]];
T[n_] := CoefficientList[b[n, n], x];
T /@ Range[0, 12] // Flatten (* Jean-François Alcover, Dec 17 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 16 2019
STATUS
approved