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A216281 Sum of n-th derivatives at x=1 of all functions that are representable as x^x^...^x with n x's and parentheses inserted in all possible ways. 3
1, 2, 21, 392, 11980, 471966, 24655820, 1548264752, 118039822488, 10482116888640, 1076582148812808, 125439212178037728, 16473767684928836256, 2410412979008498588208, 390793360308270931979400, 69716064087131957637475968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

For n=4 the A000081(4) = 4 functions and their 4th derivatives at x=1 are x^(x^3)->156, x^(x^x*x)->100, x^(x^(x^2))->80, x^(x^(x^x))->56 => a(n) = 156+100+80+56 = 392.

MAPLE

F:= proc(n) F(n):= `if`(n=1, [x], map(h->x^h, g(n-1, n-1))) end:

g:= proc(n, i) option remember; `if`(i=1, [x^n], [seq(seq(seq(

       mul(F(i)[w[t]-t+1], t=1..j)*v, w=combinat[choose](

       [$1..nops(F(i))+j-1], j)), v=g(n-i*j, i-1)), j=0..n/i)])

    end:

a:= n-> add(n!*coeff(series(subs(x=x+1, f), x, n+1), x, n), f=F(n)):

seq(a(n), n=1..12);

CROSSREFS

Row sums of A216349, A216350.

Cf. A000081, A215703.

Sequence in context: A099710 A098344 A228384 * A263625 A245686 A091315

Adjacent sequences:  A216278 A216279 A216280 * A216282 A216283 A216284

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 04 2012

EXTENSIONS

a(16) from Alois P. Heinz, May 09 2016

STATUS

approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)