A293584 Number of compositions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order and all seven letters occur at least once in the composition.

47293, 2075948, 53476920, 1058754564, 17866313444, 270907452704, 3807403790792, 50592275219138, 644225577441572, 7936529529027736, 95254972055989564, 1119634204276346052, 12939870424457764200, 147501747088827091436, 1662420626477581539972

Offset: 7

Author

Alois P. Heinz, Oct 12 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..975

Crossrefs

Column k=7 of A261781.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      add(b(n-j, k)*binomial(j+k-1, k-1), j=1..n))
    end:
a:= n-> (k->add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(7):
seq(a(n), n=7..30);

Formula

a(n) = 56*a(n-1) - 1400*a(n-2) + 20804*a(n-3) - 206864*a(n-4) + 1472576*a(n-5) - 7857468*a(n-6) + 32533654*a(n-7) - 107414264*a(n-8) + 288967984*a(n-9) - 644267912*a(n - 10) + 1206205784*a(n - 11) - 1915352424*a(n - 12) + 2598569764*a(n - 13) - 3027512680*a(n - 14) + 3038439672*a(n - 15) - 2630187744*a(n - 16) + 1962871608*a(n - 17) - 1260043528*a(n - 18) + 692851920*a(n - 19) - 324225312*a(n - 20) + 127932656*a(n - 21) - 42016752*a(n - 22) + 11279872*a(n - 23) - 2411968*a(n - 24) + 395168*a(n - 25) - 46592*a(n - 26) + 3520*a(n - 27) - 128*a(n - 28). - Vaclav Kotesovec, Oct 14 2017