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

0,3

Links

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

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.

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);

Crossrefs

Column k=10 of A305962.

Cf. A306034.

Sequence in context: A003729 A230388 A027398 * A081740 A051687 A231916

Adjacent sequences: A305967 A305968 A305969 * A305971 A305972 A305973

Keyword

nonn

Author

Alois P. Heinz, Jun 15 2018

Status

approved