|
Search: id:A116860
|
|
|
| A116860 |
|
Triangle read by rows: T(n,k) is the number of partitions into distinct odd parts with smallest part k (n>=1, k>=1). |
|
+0
3
|
|
| 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
1,50
|
|
|
COMMENT
|
Row 2 has no terms, row 2n-1 has 2n-1 terms, row 4n has 2n-1 terms, row 4n+2 for n>=1 has 2n-1 terms. Row sums are A000700. T(n,1)=A027349(n). Sum(k*T(n,k), k>=1)=A092319(n).
|
|
FORMULA
|
G.f.=sum(t^(2j-1)*x^(2j-1)*product(1+x^(2i-1), i=j+1..infinity), j=1..infinity).
|
|
EXAMPLE
|
T(25,3)=3 because we have [17,5,3], [15,7,3], and [13,9,3].
Triangle starts:
1;
{}
0,0,1;
1;
0,0,0,0,1;
1;
0,0,0,0,0,0,1;
1,0,1;
|
|
MAPLE
|
g:=sum(t^(2*j-1)*x^(2*j-1)*product(1+x^(2*i-1), i=j+1..30), j=1..30): gser:=simplify(series(g, x=0, 52)): for n from 1 to 19 do P[n]:=sort(coeff(gser, x^n)) od: d:=proc(n) if n mod 2 = 1 then n elif n=2 then 0 elif n mod 4 = 0 then n/2-1 else n/2-2 fi end: 1; {}; for n from 3 to 19 do seq(coeff(P[n], t^j), j=1..d(n)) od; # yields sequence in triangular form
|
|
CROSSREFS
|
Cf. A000700, A027349, A092319, A116857.
Adjacent sequences: A116857 A116858 A116859 this_sequence A116861 A116862 A116863
Sequence in context: A027345 A086080 A070139 this_sequence A083850 A028718 A028661
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2006
|
|
|
Search completed in 0.002 seconds
|
