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 A295106 a(n) = (1/n) times the n-th derivative of the sixth tetration of x (power tower of order 6) x^^6 at x=1. 3
 1, 1, 3, 14, 96, 849, 8642, 102941, 1373936, 20607888, 340516992, 6173590906, 121502258688, 2583247609500, 58940269686776, 1437019737587004, 37267502536335744, 1024420897710717344, 29745405670928179392, 909702365350759274304, 29224500667382460549504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..423 Eric Weisstein's World of Mathematics, Power Tower Wikipedia, Knuth's up-arrow notation Wikipedia, Tetration FORMULA a(n) = 1/n * [(d/dx)^n x^^6]_{x=1}. a(n) = (n-1)! * [x^n] (x+1)^^6. a(n) = 1/n * A211205(n). MAPLE f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end: a:= n-> (n-1)!*coeff(series(f(6), x, n+1), x, n): seq(a(n), n=1..23); MATHEMATICA f[n_] := f[n] = If[n == 0, 1, (x + 1)^f[n - 1]]; a[n_] := (n - 1)!*SeriesCoefficient[f[6], {x, 0, n}]; Array[a, 23] (* Jean-François Alcover, May 31 2018, from Maple *) CROSSREFS Column k=6 of A295028. Cf. A211205. Sequence in context: A053984 A113181 A295105 * A295107 A295108 A295109 Adjacent sequences:  A295103 A295104 A295105 * A295107 A295108 A295109 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 14 2017 STATUS approved

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Last modified September 28 09:35 EDT 2020. Contains 337394 sequences. (Running on oeis4.)