A293371 Number of partitions 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 partition.

11481, 352793, 6170486, 83317577, 941895458, 9595504513, 89629486436, 792794568624, 6679198773576, 54486400898447, 431529096734274, 3349089312506511, 25507319202685313, 191694475039884663, 1422950411887109983, 10467534744471771547, 76364568808571920303

Offset: 7

Author

Alois P. Heinz, Oct 07 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..1000

Crossrefs

Column k=7 of A261719.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
    end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(7):
seq(a(n), n=7..30);

Formula

a(n) ~ c * 7^n, where c = 3.519268129363442517546929108933080435102442778133731795486515352... - Vaclav Kotesovec, Oct 11 2017