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A305968
Number of length-n restricted growth strings (RGS) with growth <= eight and fixed first element.
3
1, 1, 9, 117, 1905, 36585, 802221, 19664325, 530764089, 15596609985, 494555435781, 16802009359677, 608027982857169, 23322183958778553, 944242763282027421, 40207158379868421429, 1795007963258388557673, 83786699444454149125041, 4079132811705470375924277
OFFSET
0,3
LINKS
FORMULA
a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..8} (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+8))
end:
a:= n-> b(n, -7):
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..8)), x, n), x, n-1)):
seq(a(n), n=0..25);
CROSSREFS
Column k=8 of A305962.
Cf. A306032.
Sequence in context: A027396 A294190 A113344 * A367473 A375722 A081629
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 15 2018
STATUS
approved