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A199296 Number of distinct values taken by 5th derivative of x^x^...^x (with n x's and parentheses inserted in all possible ways) at x=1. 10
1, 1, 2, 4, 9, 20, 45, 92, 182, 342, 601, 982, 1499, 2169, 2970, 3994, 5297, 6834, 8635, 10714, 13121, 16104, 19674, 23868, 28453, 33637, 39630, 46730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

a(4) = 4 because the A000108(3) = 5 possible parenthesizations of x^x^x^x lead to 4 different values of the 5th derivative at x=1: (x^(x^(x^x))) -> 360; (x^((x^x)^x)) -> 590; ((x^(x^x))^x), ((x^x)^(x^x)) -> 650; (((x^x)^x)^x) -> 1110.

MAPLE

f:= proc(n) option remember;

      `if`(n=1, {[0, 0, 0, 0]},

            {seq(seq(seq([2+g[1], 3*(1 +g[1] +h[1]) +g[2],

             8 +12*g[1] +6*h[1]*(1+g[1]) +4*(g[2]+h[2])+g[3],

             10+50*h[1]+10*h[2]+5*h[3]+(30+30*h[1]+10*h[2]

             +15*g[1])*g[1]+(20+10*h[1])*g[2]+5*g[3]+g[4]],

              h=f(n-j)), g=f(j)), j=1..n-1)})

    end:

a:= n-> nops(map(x-> x[4], f(n))):

seq(a(n), n=1..20);

CROSSREFS

Cf. A000081 (distinct functions), A000108 (parenthesizations), A000012 (first derivatives), A028310 (2nd derivatives), A199085 (3rd derivatives), A199205 (4th derivatives), A002845, A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A082499, A196244, A198683, A215703, A215835. Column k=5 of A216368.

Sequence in context: A024562 A087219 A214952 * A219229 A091620 A208738

Adjacent sequences:  A199293 A199294 A199295 * A199297 A199298 A199299

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 04 2011

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)