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%I #15 Oct 11 2017 10:24:05
%S 1,1,3,6,12,9,27,78,81,27,156,564,720,432,81,1110,4320,6930,5400,2025,
%T 243,8322,37260,68940,66420,34830,8748,729,70098,347382,722610,824040,
%U 541485,200718,35721,2187
%N Triangle read by rows, coefficients of polynomials in t = log(x) of the n-th derivative of x^(x^3), evaluated at x = 1. T(n, k) with n >= 0 and 0 <= k <= n.
%e Triangle start:
%e 0: [ 1]
%e 1: [ 1, 3]
%e 2: [ 6, 12, 9]
%e 3: [ 27, 78, 81, 27]
%e 4: [ 156, 564, 720, 432, 81]
%e 5: [ 1110, 4320, 6930, 5400, 2025, 243]
%e 6: [ 8322, 37260, 68940, 66420, 34830, 8748, 729]
%e 7: [70098, 347382, 722610, 824040, 541485, 200718, 35721, 2187]
%e ...
%e For n = 3, the 3rd derivative of x^(x^3) is p(3,x,t) = 27*t^3*x^6*x^(x^3) + 27*t^2*x^6*x^(x^3) + 9*t*x^6*x^(x^3) + x^6*x^(x^3) + 54*t^2*x^3*x^(x^3) + 63*t*x^3*x^(x^3) + 15*x^3*x^(x^3) + 6*t*x^(x^3) + 11*x^(x^3) where log(x) is substituted by t. Evaluated at x = 1: p(3,1,t) = 27 + 78*t + 81*t^2 + 27*t^3 with coefficients [27, 78, 81, 27].
%p # Function dx in A293472.
%p ListTools:-Flatten([seq(dx(3, n), n=0..8)]);
%t (* Function dx in A293472. *)
%t Table[dx[3, n], {n, 0, 7}] // Flatten
%Y T(n, 0) = A215704, T(n, n) = A000244.
%Y More generally, consider the n-th derivative of x^(x^m).
%Y A293472 (m=1), A293472 (m=2), this seq. (m=3).
%K sign,tabl
%O 0,3
%A _Peter Luschny_, Oct 10 2017
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