OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
Product_{k>=1} (1+a(k)*x^k) = 1 + Sum_{k>=1} k^2*x^k. - Seiichi Manyama, Jun 24 2018
EXAMPLE
From the perfect squares, construct the series 1+x+4x^2+9x^3+16x^4+25x^5+... a(1) is always the coefficient of x, here 1. Divide by (1+a(1)x), i.e. here (1+x), to get the quotient (1+a(2)x^2+...), which here gives a(2)=4. Then divide this quotient by (1+a(2)x^2), i.e. here (1+4x^2), to get (1+a(3)x^3+...), giving a(3)=5.
MATHEMATICA
terms = 34; sol = {a[1] -> 1}; Do[sol = Append[sol, Solve[ SeriesCoefficient[ x*(1+x)/(1-x)^3 - (Product[1+a[k]*x^k, {k, 1, n}] /. sol), {x, 0, n}] == 0][[1, 1]]], {n, 2, terms}];
Array[a, terms] /. sol (* Jean-François Alcover, Jun 20 2017 *)
CROSSREFS
KEYWORD
sign,look
AUTHOR
Neil Fernandez, Nov 07 2008
EXTENSIONS
Terms from a(11) on corrected by R. J. Mathar, Nov 11 2008
STATUS
approved