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A215834
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Fourth derivative of f_n at x=1, where f_n is the n-th of all functions that are representable as x^x^...^x with m>=1 x's and parentheses inserted in all possible ways.
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3
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0, 8, 52, 32, 156, 100, 80, 56, 344, 228, 148, 172, 124, 152, 104, 80, 56, 640, 440, 300, 324, 252, 220, 172, 268, 196, 148, 124, 248, 176, 128, 128, 104, 104, 80, 56, 56, 1068, 760, 536, 372, 560, 464, 396, 324, 292, 244, 196, 444, 348, 276, 252, 316, 244
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OFFSET
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1,2
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COMMENTS
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For the ordering of functions f_n see A215703.
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LINKS
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MAPLE
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T:= proc(n) T(n):=`if`(n=1, [x], map(h-> x^h, g(n-1$2))) end:
g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(
seq(mul(T(i)[w[t]-t+1], t=1..j)*v, v=g(n-i*j, i-1)), w=
combinat[choose]([$1..nops(T(i))+j-1], j)), j=0..n/i)])
end:
f:= proc() local i, l; i, l:= 0, []; proc(n) while n>
nops(l) do i:= i+1; l:= [l[], T(i)[]] od; l[n] end
end():
a:= n-> 4!*coeff(series(subs(x=x+1, f(n)), x, 5), x, 4):
seq(a(n), n=1..100);
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CROSSREFS
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Number of distinct values of a(n) taken for functions with m x's: A199205.
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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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