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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

Alois P. Heinz, Table of n, a(n) for n = 0..500

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-Fran├žois Alcover, Mar 24 2017, translated from Maple *)

CROSSREFS

Antidiagonal sums of A255903.

Sequence in context: A107086 A234643 A089846 * A131868 A272064 A000747

Adjacent sequences:  A258447 A258448 A258449 * A258451 A258452 A258453

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 30 2015

STATUS

approved

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Last modified April 25 19:05 EDT 2017. Contains 285426 sequences.