A300455 Logarithmic transform of the triangular numbers A000217.

0, 1, 2, -1, -11, 19, 201, -764, -7426, 52137, 448435, -5377604, -38712486, 777663613, 4258812299, -149524753650, -505685566184, 36733876797025, 30910872539763, -11174584391207360, 25170998506744790, 4101787001153848461, -24862093152821214653, -1776483826032814964966

Offset: 0

Author

Ilya Gutkovskiy, Mar 06 2018

Keywords

• sign

Examples

			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! + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450
• 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, Triangular Number
• Index to sequences related to polygonal numbers

Crossrefs

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

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*(i+1)/2)
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Mar 06 2018

Mathematica

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

Formula

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