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A306033
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Number of length-n restricted growth strings (RGS) with growth <= nine and first element in [9].
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3
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1, 9, 126, 2229, 46791, 1126032, 30377223, 904211997, 29347973748, 1029154793775, 38706399597879, 1551902279238186, 65998768155695109, 2964410257125490269, 140111251278756345054, 6946234487211269640633, 360202406323880296650987, 19488725004898446787394016
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: exp(Sum_{j=1..9} (exp(j*x)-1)/j).
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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+9))
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..9)), x, n+1), x, n):
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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