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

7,1

Links

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

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

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);

Crossrefs

Column k=7 of A261781.

Sequence in context: A257723 A320621 A218097 * A263067 A234708 A069370

Adjacent sequences: A293581 A293582 A293583 * A293585 A293586 A293587

Keyword

nonn

Author

Alois P. Heinz, Oct 12 2017

Status

approved