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

7,1

Links

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

Formula

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

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);

Crossrefs

Column k=7 of A261719.

Sequence in context: A023071 A349746 A100972 * A251879 A201048 A236522

Adjacent sequences: A293368 A293369 A293370 * A293372 A293373 A293374

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2017

Status

approved