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A305967
Number of length-n restricted growth strings (RGS) with growth <= seven and fixed first element.
3
1, 1, 8, 92, 1324, 22464, 435044, 9416240, 224382116, 5820361008, 162900823428, 4884515258224, 155992931417316, 5280138035455024, 188639017788288836, 7087660960768335472, 279189959071013966500, 11498108706476961892400, 493881446025566760548100
OFFSET
0,3
LINKS
FORMULA
a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..7} (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+7))
end:
a:= n-> b(n, -6):
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..7)), x, n), x, n-1)):
seq(a(n), n=0..25);
CROSSREFS
Column k=7 of A305962.
Cf. A306031.
Sequence in context: A027395 A277307 A255520 * A113353 A081624 A298188
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 15 2018
STATUS
approved