OFFSET
2,8
COMMENTS
LINKS
Alois P. Heinz, Rows n = 2..200, flattened
W. Lang and M. Sjodahl, First 20 rows of the array and row sums.
FORMULA
a(n,m) = sum over entries of A145573(n,k) array which belong to partitions with part number m, for m=1..floor(n/2)). Note that partitions with parts number m>floor(n/2) have always at least one part 1.
G.f.: Product_{i>=2} 1/(1- y*x^i). - Geoffrey Critzer, Sep 23 2012
EXAMPLE
1;
1;
1, 1;
1, 1;
1, 2, 1;
1, 2, 1;
1, 3, 2, 1;
1, 3, 3, 1;
1, 4, 4, 2, 1;
MAPLE
b:= proc(n, i, t) option remember; `if`(2*t>n or t*i<n, 0,
`if`(n=0, 1, `if`(i<2, 0, b(n, i-1, t) +b(n-i, i, t-1))))
end:
a:= (n, m)-> b(n, n, m):
seq(seq(a(n, m), m=1..iquo(n, 2)), n=2..30); # Alois P. Heinz, Oct 18 2012
MATHEMATICA
nn=15; f[list_]:=Select[list, #>0&]; p=Product[1/(1-y x^i), {i, 2, nn}]; Drop[Map[f, CoefficientList[Series[p, {x, 0, nn}], {x, y}]], 1]//Grid (* Geoffrey Critzer, Sep 23 2012 *)
PROG
(Sage) # Prints the table; cf. A011973.
for n in (2..20): [Partitions(n, length=m, min_part=2).cardinality() for m in (1..n//2)] # Peter Luschny, Oct 18 2012
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang and Malin Sjodahl, Mar 06 2009
STATUS
approved