A300452 Logarithmic transform of the cubes A000578.

0, 1, 7, 5, -146, -351, 9936, 51421, -1394000, -12844287, 328407400, 4874111901, -115361217696, -2607873466511, 55768370301112, 1866984952934445, -34886452149332864, -1720211491314549375, 26716801597874981064, 1979492625918149729437, -23490293022369696366560, -2777285149336544358953679

Offset: 0

Author

Ilya Gutkovskiy, Mar 06 2018

Keywords

• sign

Examples

			E.g.f.: A(x) = x/1! + 7*x^2/2! + 5*x^3/3! - 146*x^4/4! - 351*x^5/5! + 9936*x^6/6! + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..408
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
• M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Logarithmic Transform
• Eric Weisstein's World of Mathematics, Cubic Number

Crossrefs

Cf. A000578, A009306, A033464, A279358.

Programs

Maple

a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
      binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->i^3)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 06 2018

Mathematica

nmax = 21; CoefficientList[Series[Log[1 + Exp[x] x (1 + 3 x + x^2)], {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: log(1 + exp(x)*x*(1 + 3*x + x^2)).