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A215834 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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For the ordering of functions f_n see A215703.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..7813

MAPLE

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);

CROSSREFS

Row n=4 of A215703.

Number of distinct values of a(n) taken for functions with m x's: A199205.

Cf. A000081, A087803.

Sequence in context: A226199 A267637 A238648 * A180319 A199706 A302318

Adjacent sequences:  A215831 A215832 A215833 * A215835 A215836 A215837

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 24 2012

STATUS

approved

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Last modified September 23 21:27 EDT 2020. Contains 337315 sequences. (Running on oeis4.)