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

Author

Alois P. Heinz, Jun 15 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=5 of A305962.

Cf. A306029.

Programs

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);

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.