A305965 Number of length-n restricted growth strings (RGS) with growth <= five and fixed first element.

1, 1, 6, 51, 541, 6756, 96205, 1530025, 26775550, 509861195, 10472109149, 230368347780, 5396308081285, 133949699318945, 3508794554854054, 96648143868171171, 2790590111082279405, 84231759174460743700, 2651416546964399982909, 86848041397350751409257

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..444

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..5} (exp(j*x)-1)/j) for n>0, a(0) = 1.

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+5))
    end:
a:= n-> b(n, -4):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> `if`(n=0, 1, (n-1)!*coeff(series(exp(x+add(
           (exp(j*x)-1)/j, j=1..5)), x, n), x, n-1)):
seq(a(n), n=0..25);

Crossrefs

Column k=5 of A305962.

Cf. A306029.

Sequence in context: A263895 A027393 A346766 * A255518 A208250 A253097

Adjacent sequences: A305962 A305963 A305964 * A305966 A305967 A305968

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved