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

Author

Alois P. Heinz, Aug 24 2012

Keywords

• nonn

Comments

For the ordering of functions f_n see A215703.

Links

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

Crossrefs

Row n=4 of A215703.

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

Cf. A000081, A087803.

Programs

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);