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A300452 Logarithmic transform of the cubes A000578.

%I A300452 #13 Feb 16 2025 08:33:53
%S A300452 0,1,7,5,-146,-351,9936,51421,-1394000,-12844287,328407400,4874111901,
%T A300452 -115361217696,-2607873466511,55768370301112,1866984952934445,
%U A300452 -34886452149332864,-1720211491314549375,26716801597874981064,1979492625918149729437,-23490293022369696366560,-2777285149336544358953679
%N A300452 Logarithmic transform of the cubes A000578.
%H A300452 Alois P. Heinz, <a href="/A300452/b300452.txt">Table of n, a(n) for n = 0..408</a>
%H A300452 M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A300452 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A300452 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A300452 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogarithmicTransform.html">Logarithmic Transform</a>
%H A300452 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%F A300452 E.g.f.: log(1 + exp(x)*x*(1 + 3*x + x^2)).
%e A300452 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! + ...
%p A300452 a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*
%p A300452       binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->i^3)
%p A300452     end:
%p A300452 seq(a(n), n=0..25);  # _Alois P. Heinz_, Mar 06 2018
%t A300452 nmax = 21; CoefficientList[Series[Log[1 + Exp[x] x (1 + 3 x + x^2)], {x, 0, nmax}], x] Range[0, nmax]!
%Y A300452 Cf. A000578, A009306, A033464, A279358.
%K A300452 sign
%O A300452 0,3
%A A300452 _Ilya Gutkovskiy_, Mar 06 2018