A327678 Number of colored compositions of 2n using all colors of an n-set such that all parts have different color patterns and the patterns for parts i are sorted and have i colors (in arbitrary order).

1, 1, 60, 7512, 1546042, 541742985, 267920998650, 180675370176420, 160654598650809964, 178879511446386682365, 243695196628845859469020, 400544315906804782687318938, 777083567062772102871149374020, 1755895011129198763056241198051342

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Formula

a(n) = A327673(2n,n).

Maple

b:= proc(n, i, k, p) option remember;
     `if`(n=0, p!, `if`(i<1, 0, add(binomial(k^i, j)*
      b(n-i*j, min(n-i*j, i-1), k, p+j)/j!, j=0..n/i)))
    end:
a:= n-> add(b(2*n$2, i, 0)*(-1)^(n-i)*binomial(n, i), i=0..n):
seq(a(n), n=0..15);

Mathematica

b[n_, i_, k_, p_] := b[n, i, k, p] =
     If[n == 0, p!, If[i < 1, 0, Sum[Binomial[k^i, j]*
     b[n - i*j, Min[n - i*j, i - 1], k, p + j]/j!, {j, 0, n/i}]]];
a[n_] := Sum[b[2n, 2n, i, 0]*(-1)^(n-i)*Binomial[n, i], {i, 0, n}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 11 2022, after Alois P. Heinz *)

Crossrefs

Cf. A327673.

Sequence in context: A091753 A336629 A303790 * A130214 A295815 A146498

Adjacent sequences: A327675 A327676 A327677 * A327679 A327680 A327681

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2019

Status

approved