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A306028
Number of length-n restricted growth strings (RGS) with growth <= four and first element in [4].
4
1, 4, 26, 214, 2096, 23578, 297692, 4150798, 63148652, 1038505282, 18324165284, 344791676446, 6883214479964, 145160792680210, 3221934217192772, 75022325591768782, 1827426669105650588, 46448931646662304066, 1229212096172351894852, 33800410177112965182910
OFFSET
0,2
LINKS
FORMULA
E.g.f.: exp(Sum_{j=1..4} (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+4))
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..4)), x, n+1), x, n):
seq(a(n), n=0..25);
CROSSREFS
Column k=4 of A306024.
Cf. A305964.
Sequence in context: A355379 A349719 A283828 * A164101 A048351 A224734
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 17 2018
STATUS
approved