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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.
3
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
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.
Sequence in context: A159497 A177595 A013922 * A006423 A067423 A221099
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 24 2012
STATUS
approved