OFFSET
1,4
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
N. J. A. Sloane, Transforms
EXAMPLE
T(5,1) = ([1,2,4]*[1,1,4] + [1]*[1]*4 + [1,2]*[1,1]*2 + [1,3]*[1,2]*1)/4 = 36/4 = 9.
Triangle begins:
1;
1, 1;
2, 1, 1;
4, 2, 1, 1;
9, 3, 2, 1, 1;
20, 6, 3, 2, 1, 1;
48, 10, 5, 3, 2, 1, 1;
115, 20, 8, 5, 3, 2, 1, 1;
286, 36, 14, 7, 5, 3, 2, 1, 1;
719, 72, 23, 12, 7, 5, 3, 2, 1, 1;
MAPLE
etrk:= proc(p) proc(n, k) option remember; `if`(n=0, 1,
add(add(d*p(d, k), d=numtheory[divisors](j))*
procname(n-j, k), j=1..n)/n)
end end:
B:= etrk(T):
T:= (n, k)-> `if`(n<=k, `if`(n=0, 0, 1), B(n-k, k)):
seq(seq(T(n, k), k=1..n), n=1..14);
MATHEMATICA
etrk[p_] := Module[{f}, f[n_, k_] := f[n, k] = If[n == 0, 1, (Sum[Sum[d*p[d, k], {d, Divisors[j]}]*f[n-j, k], {j, 1, n-1}] + Sum[d*p[d, k], {d, Divisors[n]}])/n]; f]; b = etrk[t]; t[n_, k_] := If[n <= k, If[n == 0, 0, 1], b[n-k, k]]; Table[t[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 01 2013, after Alois P. Heinz *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Sep 07 2008
STATUS
approved