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A305964
Number of length-n restricted growth strings (RGS) with growth <= four and fixed first element.
3
1, 1, 5, 35, 305, 3125, 36479, 475295, 6811205, 106170245, 1784531879, 32117927231, 615413731205, 12493421510405, 267608512061159, 6026688403933967, 142256385130774229, 3509899012049396645, 90301862963332188839, 2417349828110572405823, 67201548131159391828677
OFFSET
0,3
LINKS
FORMULA
a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..4} (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+4))
end:
a:= n-> b(n, -3):
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..4)), x, n), x, n-1)):
seq(a(n), n=0..25);
CROSSREFS
Column k=4 of A305962.
Cf. A306028.
Sequence in context: A346765 A177354 A253096 * A226739 A109253 A052797
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 15 2018
STATUS
approved