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A305966
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Number of length-n restricted growth strings (RGS) with growth <= six and fixed first element.
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3
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1, 1, 7, 70, 875, 12887, 216552, 4065775, 84022595, 1889844292, 45857269017, 1191971998455, 32996489835190, 968034453578997, 29972909437783507, 975944207096597110, 33313664777283768535, 1188852507118147925627, 44246989258071738375272, 1713739685432232160181115
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (n-1)! * [x^(n-1)] exp(x+Sum_{j=1..6} (exp(j*x)-1)/j) for n>0, a(0) = 1.
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0, 1,
add(b(n-1, max(m, j)), j=1..m+6))
end:
a:= n-> b(n, -5):
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..6)), x, n), x, n-1)):
seq(a(n), n=0..25);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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