|
Search: id:A116861
|
|
|
| A116861 |
|
Triangle read by rows: T(n,k) is the number of partitions of n such that the sum of the parts, counted without multiplicities, is equal to k (n>=1, k>=1). |
|
+0
1
|
|
| 1, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 0, 2, 1, 3, 1, 1, 3, 1, 1, 4, 1, 0, 3, 2, 2, 2, 5, 1, 1, 3, 3, 2, 4, 2, 6, 1, 0, 5, 2, 3, 4, 4, 3, 8, 1, 1, 4, 3, 4, 7, 4, 5, 3, 10, 1, 0, 5, 3, 4, 7, 7, 6, 6, 5, 12, 1, 1, 6, 4, 3, 12, 6, 8, 7, 9, 5, 15, 1, 0, 6, 4, 5, 10, 10, 9, 10, 11, 10, 7, 18, 1, 1, 6, 4, 5, 15, 11, 13
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
COMMENT
|
Row sums yield A000041 (the partition numbers). T(n,n)=A000009(n) Sum(k*T(n,k),k=1..n)=A014153(n-1).
|
|
FORMULA
|
G.f.= -1 + product(1+t^j*x^j/(1-x^j), j=1..infinity).
|
|
EXAMPLE
|
T(10,7)=4 because we have [6,1,1,1,1],[4,3,3],[4,2,2,1,1], and [4,2,1,1,1,1] (6+1=4+3=4+2+1=7).
Triangle starts:
1;
1,1;
1,0,2;
1,1,1,2;
1,0,2,1,3;
1,1,3,1,1,4;
|
|
MAPLE
|
g:=-1+product(1+t^j*x^j/(1-x^j), j=1..40): gser:=simplify(series(g, x=0, 18)): for n from 1 to 14 do P[n]:=sort(coeff(gser, x^n)) od: for n from 1 to 14 do seq(coeff(P[n], t^j), j=1..n) od; # yields sequence in triangular form
|
|
CROSSREFS
|
Cf. A000041, A000009, A014153.
Adjacent sequences: A116858 A116859 A116860 this_sequence A116862 A116863 A116864
Sequence in context: A035180 A092673 A112400 this_sequence A105242 A114116 A054532
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
|
|
|
Search completed in 0.002 seconds
|
