OFFSET
0,3
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
FORMULA
E.g.f.: log(1 + exp(x)*x*(x + 2)/2).
EXAMPLE
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! + ...
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]!
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Mar 06 2018
STATUS
approved