A293474 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.

1, 1, 3, 6, 12, 9, 27, 78, 81, 27, 156, 564, 720, 432, 81, 1110, 4320, 6930, 5400, 2025, 243, 8322, 37260, 68940, 66420, 34830, 8748, 729, 70098, 347382, 722610, 824040, 541485, 200718, 35721, 2187

Offset: 0

Author

Peter Luschny, Oct 10 2017

Keywords

• sign
• tabl

Examples

			Triangle start:
0: [    1]
1: [    1,      3]
2: [    6,     12,      9]
3: [   27,     78,     81,     27]
4: [  156,    564,    720,    432,     81]
5: [ 1110,   4320,   6930,   5400,   2025,    243]
6: [ 8322,  37260,  68940,  66420,  34830,   8748,   729]
7: [70098, 347382, 722610, 824040, 541485, 200718, 35721, 2187]
...
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].
		

Crossrefs

T(n, 0) = A215704, T(n, n) = A000244.

More generally, consider the n-th derivative of x^(x^m).

A293472 (m=1), A293472 (m=2), this seq. (m=3).

Programs

Maple

# Function dx in A293472.
ListTools:-Flatten([seq(dx(3, n), n=0..8)]);

Mathematica

(* Function dx in A293472. *)
Table[dx[3, n], {n, 0, 7}] // Flatten