A261828 Number of compositions of 2n into distinct parts where each part i is marked with a word of length i over an n-ary alphabet whose letters appear in alphabetical order and all n letters occur at least once in the composition.

1, 1, 15, 832, 14791, 2008546, 55380132, 2868333476, 511805155863, 31512728488918, 2638310862477610, 926651539894899446, 74254761492776175196, 6851495812540548188072, 9541620342114654822145972, 611287722968440282212322702, 58354641005988089624088037623

Offset: 0

Author

Alois P. Heinz, Sep 02 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A261784, A261836.

Programs

Maple

b:= proc(n, i, p, k) option remember;
      `if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
    end:
a:= n-> add(b(2*n$2, 0, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..20);

Mathematica

b[n_, i_, p_, k_] := b[n, i, p, k] = If[i*(i+1)/2n, 0, b[n-i, i-1, p+1, k]*Binomial[i+k-1, k-1]]]]; a[n_] := Sum[b[2*n, 2*n, 0, n-i]*(-1)^i*Binomial[n, i], {i, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)

Formula

a(n) = A261836(2n,n).