A281434 Number of terms in the fully expanded n-th derivative of x^(x^x).

1, 3, 12, 30, 64, 113, 188, 285, 415, 577, 780, 1017, 1312, 1648, 2044, 2489, 3008, 3583, 4236, 4953, 5760, 6638, 7611, 8664, 9822, 11069, 12426, 13880, 15455, 17131, 18940, 20855, 22912, 25083, 27404, 29844, 32448, 35178, 38075, 41109, 44320, 47672, 51212

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Example

For n=1, the 1st derivative of x^(x^x) is x^(x^x+x-1) + x^(x^x+x)*log(x) + x^(x^x+x)*log^2(x), so a(1) = 3.

Mathematica

Join[{1}, Length /@ Rest[NestList[Expand[D[#, x]] &, x^x^x, 42]]]

Crossrefs

Cf. A293239.

Sequence in context: A135503 A048088 A064181 * A296289 A089143 A073952

Adjacent sequences: A281431 A281432 A281433 * A281435 A281436 A281437

Keyword

nonn

Author

Vladimir Reshetnikov, Oct 05 2017

Status

approved