The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216350 Triangle T(n,k) in which n-th row lists in increasing order the values of the n-th derivative at x=1 of all functions that are representable as x^x^...^x with n x's and parentheses inserted in all possible ways; n>=1, 1<=k<=A000081(n). 8
 1, 2, 9, 12, 56, 80, 100, 156, 480, 660, 890, 950, 1180, 1360, 1420, 1880, 3160, 5094, 6534, 8874, 10848, 10974, 13014, 13314, 14928, 14988, 15114, 20268, 21474, 22008, 24042, 29682, 31968, 34974, 35382, 50496, 87990, 65534, 78134, 102494, 131684, 141974 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..12, flattened 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 => 4th row = [56, 80, 100, 156]. Triangle T(n,k) begins: : 1; : 2; : 9, 12; : 56, 80, 100, 156; : 480, 660, 890, 950, 1180, 1360, 1420, 1880, 3160; : 5094, 6534, 8874, 10848, 10974, 13014, 13314, 14928, 14988, 15114, ... MAPLE with(combinat): F:= proc(n) F(n):= `if`(n<2, [x\$n], map(h->x^h, g(n-1, n-1))) end: g:= proc(n, i) option remember; `if`(n=0 or i=1, [x^n], `if`(i<1, [], [seq(seq(seq(mul(F(i)[w[t]-t+1], t=1..j)*v, w=choose([\$1..nops(F(i))+j-1], j)), v=g(n-i*j, i-1)), j=0..n/i)])) end: T:= n-> sort(map(f-> n!*coeff(series(subs(x=x+1, f) , x, n+1), x, n), F(n)))[]: seq(T(n), n=1..7); CROSSREFS First column gives: A033917. Last elements of rows give: A216351. A version with different ordering of row elements is: A216349. Rows sums give: A216281. Cf. A000081, A215703. Sequence in context: A076505 A218073 A129345 * A125019 A259984 A225548 Adjacent sequences: A216347 A216348 A216349 * A216351 A216352 A216353 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Sep 04 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)