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 A300455 Logarithmic transform of the triangular numbers A000217. 2

%I

%S 0,1,2,-1,-11,19,201,-764,-7426,52137,448435,-5377604,-38712486,

%T 777663613,4258812299,-149524753650,-505685566184,36733876797025,

%U 30910872539763,-11174584391207360,25170998506744790,4101787001153848461,-24862093152821214653,-1776483826032814964966

%N Logarithmic transform of the triangular numbers A000217.

%H Alois P. Heinz, <a href="/A300455/b300455.txt">Table of n, a(n) for n = 0..450</a>

%H 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 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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LogarithmicTransform.html">Logarithmic Transform</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>

%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>

%F E.g.f.: log(1 + exp(x)*x*(x + 2)/2).

%e E.g.f.: A(x) = x/1! + 2*x^2/2! - x^3/3! - 11*x^4/4! + 19*x^5/5! + 201*x^6/6! - 764*x^7/7! - 7426*x^8/8! + ...

%p a:= proc(n) option remember; (t-> `if`(n=0, 0, t(n) -add(j*

%p binomial(n, j)*t(n-j)*a(j), j=1..n-1)/n))(i->i*(i+1)/2)

%p end:

%p seq(a(n), n=0..25); # _Alois P. Heinz_, Mar 06 2018

%t nmax = 23; CoefficientList[Series[Log[1 + Exp[x] x (x + 2)/2], {x, 0, nmax}], x] Range[0, nmax]!

%Y Cf. A000217, A009306, A033464, A279361, A300452.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Mar 06 2018

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Last modified April 4 05:15 EDT 2020. Contains 333212 sequences. (Running on oeis4.)