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.

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

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: A267637 A238648 A341626 * A180319 A199706 A302318

Adjacent sequences: A215831 A215832 A215833 * A215835 A215836 A215837

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2012

Status

approved