OFFSET
0,10
COMMENTS
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
G.f.: Product_{j>=1} (1+x^(2*j-1))*(1+t*x^(2*j)).
EXAMPLE
T(9,2)=2 because we have [6,2,1] and [4,3,2].
Triangle starts:
1;
1;
0, 1;
1, 1;
1, 1;
1, 2;
1, 2, 1;
1, 3, 1;
MAPLE
g:=product((1+x^(2*j-1))*(1+t*x^(2*j)), j=1..25): gser:=simplify(series(g, x=0, 38)): P[0]:=1: for n from 1 to 27 do P[n]:=sort(coeff(gser, x^n)) od: for n from 0 to 27 do seq(coeff(P[n], t, j), j=0..floor((sqrt(1+4*n)-1)/2)) od; # yields sequence in triangular form
MATHEMATICA
With[{m=25}, CoefficientList[CoefficientList[Series[Product[(1+x^(2*j- 1))*(1+t*x^(2*j)), {j, 1, m+2}], {x, 0, m}, {t, 0, m}], x], t]]//Flatten (* G. C. Greubel, Jun 07 2019 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Feb 22 2006
STATUS
approved