OFFSET
0,6
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..1000, flattened
FORMULA
G.f.: Product_{k>=1} (1 - x^prime(k))/(1 - x^k)*(y/(1-x^prime(k)) - y + 1).
EXAMPLE
T(6,1) = 7 because we have: 5+1, 4+2, 3+3, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1+1.
Triangle T(n,k) begins:
1;
1;
1, 1;
1, 2;
2, 3;
2, 4, 1;
3, 7, 1;
3, 9, 3;
5, 12, 5;
6, 15, 9;
8, 22, 11, 1;
...
MAPLE
b:= proc(n, i) option remember; expand(
`if`(n=0, 1, `if`(i<1, 0, add(b(n-i*j, i-1)*
`if`(j>0 and isprime(i), x, 1), j=0..n/i))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)):
seq(T(n), n=0..30); # Alois P. Heinz, Jun 26 2016
MATHEMATICA
nn = 20; Map[Select[#, # > 0 &] &, CoefficientList[Series[Product[
1/(1 - z^k), {k, Select[Range[1000], PrimeQ[#] == False &]}] Product[
u/(1 - z^j) - u + 1, {j, Table[Prime[n], {n, 1, nn}]}], {z, 0,
nn}], {z, u}]] // Grid
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Jun 25 2016
STATUS
approved