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 A295103 a(n) = (1/n) times the n-th derivative of the third tetration of x (power tower of order 3) x^^3 at x=1. 3
 1, 1, 3, 8, 36, 159, 932, 5627, 40016, 302364, 2510712, 22623490, 213486864, 2227719948, 23388469400, 277570328040, 3182959484736, 42530335589088, 523078873327872, 7846745537655360, 101370634558327680, 1717052148685665792, 22657314273376353408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS First term < 0: a(33) = -26329560314038014690778779463680. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..453 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^^3]_{x=1}. a(n) = (n-1)! * [x^n] (x+1)^^3. a(n) = 1/n * A179230(n). MAPLE f:= proc(n) f(n):= `if`(n=0, 1, (x+1)^f(n-1)) end: a:= n-> (n-1)!*coeff(series(f(3), 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[3], {x, 0, n}]; Array[a, 23] (* Jean-François Alcover, May 31 2018, from Maple *) CROSSREFS Column k=3 of A295028. Cf. A179230. Sequence in context: A026649 A148919 A087905 * A299329 A020111 A111543 Adjacent sequences:  A295100 A295101 A295102 * A295104 A295105 A295106 KEYWORD sign AUTHOR Alois P. Heinz, Nov 14 2017 STATUS approved

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Last modified September 28 09:40 EDT 2020. Contains 337393 sequences. (Running on oeis4.)