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A065048
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Largest unsigned Stirling number of the first kind: max_k(s(n+1,k)); i.e., largest coefficient of polynomial x*(x+1)*(x+2)*(x+3)*...*(x+n).
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9
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1, 1, 3, 11, 50, 274, 1764, 13132, 118124, 1172700, 12753576, 150917976, 1931559552, 26596717056, 392156797824, 6165817614720, 102992244837120, 1821602444624640, 34012249593822720, 668609730341153280, 13803759753640704000, 298631902863216384000
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OFFSET
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0,3
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COMMENTS
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n! <= a(n) <= (n+1)!; n <= a(n+1)/a(n) <= (n+1). - Max Alekseyev, Jul 17 2019
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LINKS
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FORMULA
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EXAMPLE
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a(4)=50 since polynomial is x^4 + 10*x^3 + 35*x^2 + 50*x + 24.
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MAPLE
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P:= x: A[0]:= 1:
for n from 1 to 50 do
P:= expand(P*(x+n));
A[n]:= max(coeffs(P, x));
od:
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MATHEMATICA
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a[n_] := Max[Array[Abs[StirlingS1[n+1, #]]&, n+1]];
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PROG
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(PARI) a(n) = if (n==0, 1, vecmax(vector(n, k, abs(stirling(n+1, k, 1))))); \\ Michel Marcus, Jul 04 2016; corrected Jun 12 2022
(Python)
from collections import Counter
c = {1:1}
for k in range(1, n+1):
d = Counter()
for j in c:
d[j] += k*c[j]
d[j+1] += c[j]
c = d
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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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