A215835 Fifth 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, 10, 240, 180, 1110, 650, 590, 360, 3160, 1880, 1180, 1420, 950, 1360, 890, 660, 480, 7050, 4410, 2770, 3130, 2300, 2070, 1480, 2670, 1840, 1370, 1070, 2610, 1780, 1190, 1310, 1010, 1080, 780, 600, 480, 13560, 8900, 5780, 3780, 6260, 4950, 4140, 3190, 3080

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-> 5!*coeff(series(subs(x=x+1, f(n)), x, 6), x, 5):
seq(a(n), n=1..100);

Crossrefs

Row n=5 of A215703.

Number of distinct values of a(n) taken for functions with m x's: A199296.

Cf. A000081, A087803.

Sequence in context: A159497 A177595 A013922 * A006423 A067423 A221099

Adjacent sequences: A215832 A215833 A215834 * A215836 A215837 A215838

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2012

Status

approved