OFFSET
0,12
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..600, flattened
FORMULA
G.f.: product(1+tx^(2j-1)+x^(4j-2)/(1-x^(2j-1)), j=1..infinity).
EXAMPLE
T(10,2) = 3 because the only partitions of 10 into odd parts and having exactly 2 parts that appear only once are [9,1],[7,3] and [5,3,1,1].
Triangle starts:
1;
0, 1;
1, 0;
1, 1;
1, 0, 1;
1, 2, 0;
2, 1, 1;
1, 4, 0;
MAPLE
g:=product(1+t*x^(2*j-1)+x^(2*(2*j-1))/(1-x^(2*j-1)), j=1..30): gser:=simplify(series(g, x=0, 30)): P[0]:=1: for n from 1 to 25 do P[n]:=coeff(gser, x^n) od: for n from 0 to 25 do seq(coeff(P[n], t, j), j=0..floor(sqrt(n))) od; # yields sequence in triangular form, with one extra 0 in some rows
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
expand(add(b(n-i*j, i-2)*`if`(j=1, x, 1), j=0..n/i))))
end:
T:= n-> (p-> seq(coeff(p, x, k), k=0..floor(sqrt(n))))
(b(n, n-irem(n+1, 2))):
seq(T(n), n=0..25); # Alois P. Heinz, Mar 16 2014
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Expand[Sum[b[n-i*j, i-2]*If[j == 1, x, 1], {j, 0, n/i}]]]]; T[n_] := Function[{p}, Table[Coefficient[p, x, k], {k, 0, Floor[Sqrt[n]]}]][b[n, n-Mod[n+1, 2]]]; Table[T[n], {n, 0, 25}] // Flatten (* Jean-François Alcover, May 13 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Feb 22 2006
STATUS
approved