A305970 Number of length-n restricted growth strings (RGS) with growth <= ten and fixed first element.

1, 1, 11, 176, 3531, 83611, 2261534, 68402389, 2278643499, 82654180884, 3235722405487, 135734461882371, 6065518222891786, 287319811049356921, 14366920922020964539, 755605044476363993912, 41667154360185375211619, 2402483802700920413411739

Offset: 0

Author

Alois P. Heinz, Jun 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Column k=10 of A305962.

Cf. A306034.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, 1,
      add(b(n-1, max(m, j)), j=1..m+10))
    end:
a:= n-> b(n, -9):
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..10)), x, n), x, n-1)):
seq(a(n), n=0..25);

Formula

a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..10} (exp(j*x)-1)/j) for n>0, a(0) = 1.