OFFSET
1,2
COMMENTS
FORMULA
G.f.: G(t,x) = Sum_{i>=1} x^i/(1-x^i) + Sum_{i>=1} Sum_{j>=i+1} x^(i+j)/(1-x^i)/(1-x^j)/Product_{k=i+1..j-1} (1-tx^k).
EXAMPLE
T(8,2) = 1 because among the 22 partitions of 8 only [3,2,2,1] has 2 parts strictly between the smallest and the largest part.
Triangle starts:
1;
2;
3;
5;
7;
10, 1;
13, 2;
MAPLE
g := add(x^i/(1-x^i), i=1..80)+add(add(x^(i+j)/((1-x^i)*(1-x^j)*mul(1-t*x^k, k=i+1..j-1)), j=i+1..80), i=1..80): gser := simplify(series(g, x=0, 23)): for n to 22 do P[n]:= sort(coeff(gser, x, n)) end do: for n to 22 do seq(coeff(P[n], t, k), k=0..degree(P[n])) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Dec 25 2015
STATUS
approved