OFFSET
1,2
COMMENTS
Compare g.f. to the Lambert series identity: Sum_{n>=1} n^3*x^n/(1-x^n) = Sum_{n>=1} sigma_3(n)*x^n.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
G.f.: A(x) = x + 18*x^2 + 140*x^3 + 876*x^4 + 3654*x^5 + 17640*x^6 + ...
where A(x) = x/(1-2*x-x^2) + 2^3*2*x^2/(1-6*x^2+x^4) + 3^3*5*x^3/(1-14*x^3-x^6) + 4^3*12*x^4/(1-34*x^4+x^8) + 5^3*29*x^5/(1-82*x^5-x^10) + 6^3*70*x^6/(1-198*x^6+x^12) + ... + n^3*Pell(n)*x^n/(1 - A002203(n)*x^n + (-1)^n*x^(2*n)) + ...
MATHEMATICA
Table[DivisorSigma[3, n] Fibonacci[n, 2], {n, 1, 50}] (* G. C. Greubel, Jan 05 2018 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 14 2012
STATUS
approved