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A306029
Number of length-n restricted growth strings (RGS) with growth <= five and first element in [5].
3
1, 5, 40, 405, 4875, 67354, 1044045, 17867125, 333554020, 6730070329, 145676361731, 3362266525430, 82326965117385, 2129349953723509, 57961263778376192, 1655067729384150829, 49437118345913831595, 1540860755766376984434, 50000885646431513577973
OFFSET
0,2
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..5} (exp(j*x)-1)/j).
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, 0):
seq(a(n), n=0..25);
# second Maple program:
a:= n-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..5)), x, n+1), x, n):
seq(a(n), n=0..25);
CROSSREFS
Column k=5 of A306024.
Cf. A305965.
Sequence in context: A061633 A371372 A143437 * A243671 A375456 A083304
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 17 2018
STATUS
approved