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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..460

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

Adjacent sequences: A305961 A305962 A305963 * A305965 A305966 A305967

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2018

STATUS

approved

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)