login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A258450 Number of collections of nonempty multisets of colored objects, where n is the number of objects plus the number of distinct colors. 2
1, 0, 1, 2, 5, 13, 35, 100, 298, 926, 2995, 10045, 34871, 125040, 462283, 1759340, 6882479, 27639252, 113809750, 479993898, 2071411798, 9138568984, 41182104446, 189418562699, 888607018626, 4248949407337, 20695172225549, 102617378820155, 517728263280060 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = Sum_{i=0..floor(n/2)} A255903(n-i,i).
EXAMPLE
a(4) = 5: {{1},{1},{1}}, {{1},{1,1}}, {{1,1,1}}, {{1},{2}}, {{1,2}}.
MAPLE
with(numtheory):
A:= proc(n, k) option remember; `if`(n=0, 1, add(A(n-j, k)*
add(d*binomial(d+k-1, k-1), d=divisors(j)), j=1..n)/n)
end:
T:= (n, k)-> add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k):
a:= n-> add(T(n-i, i), i=0..n/2):
seq(a(n), n=0..30);
MATHEMATICA
A[n_, k_] := A[n, k] = If[n==0, 1, Sum[A[n-j, k]*DivisorSum[j, #*Binomial[# +k-1, k-1]&], {j, 1, n}]/n];
T[n_, k_] := Sum[A[n, k-i]*(-1)^i*Binomial[k, i], {i, 0, k}];
a[n_] := Sum[T[n-i, i], {i, 0, n/2}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 24 2017, translated from Maple *)
CROSSREFS
Antidiagonal sums of A255903.
Sequence in context: A294790 A234643 A089846 * A131868 A339294 A272064
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 30 2015
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 17:59 EDT 2024. Contains 371693 sequences. (Running on oeis4.)