A306031 Number of length-n restricted growth strings (RGS) with growth <= seven and first element in [7].

1, 7, 77, 1071, 17689, 335083, 7117789, 166862583, 4266097185, 117856459427, 3492369757317, 110332338885167, 3697474419284233, 130877053323860507, 4875005854140483629, 190478720135836588519, 7784916624799021983345, 331981949761308979115795

Offset: 0

Author

Alois P. Heinz, Jun 17 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..421

Crossrefs

Column k=7 of A306024.

Cf. A305967.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+7))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..7)), x, n+1), x, n):
seq(a(n), n=0..25);

Formula

E.g.f.: exp(Sum_{j=1..7} (exp(j*x)-1)/j).