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

0,3

Links

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

Formula

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

Maple

b:= proc(n, i, p, k) option remember;
      `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
      `if`(i>n, 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)/2<n, 0, If[n==0, p!, b[n, i - 1, p, k] + If[i>n, 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 *)

Crossrefs

Cf. A261784, A261836.

Sequence in context: A301312 A230181 A187803 * A205432 A020240 A281695

Adjacent sequences: A261825 A261826 A261827 * A261829 A261830 A261831

Keyword

nonn

Author

Alois P. Heinz, Sep 02 2015

Status

approved