A015718 Triangular array T given by rows: T(n,k) = number of partitions of n into distinct parts, none of which is k (1<=k<=n).

0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 7, 7, 8, 9, 9, 9, 10, 10, 11, 11, 11, 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 14, 10, 11, 12

Offset

1,8

Links

Table of n, a(n) for n=1..81.

Example

T(7,4)=3 because among the 5 partitions of 7 into distinct parts, only [7],[6,1] and [5,2] do not contain the part 4.
Triangle starts:
0;
1,0;
1,1,1;
1,2,1,1;
2,2,2,2,2;
2,2,3,3,3,3;
3,3,4,3,4,4,4;

Maple

g:=product(1+x^i, i=1..30)*sum(t^j/(1+x^j), j=1..50): gser:=simplify(series(g, x=0, 18)): for n from 1 to 16 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 14 do seq(coeff(P[n], t^k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch, Apr 15 2006

Crossrefs

Sequence in context: A256945 A282091 A354110 * A008350 A019556 A165640

Adjacent sequences: A015715 A015716 A015717 * A015719 A015720 A015721

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved