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A163318 Expansion of g.f.: Product_{k>=1} 1+k*x^k/(1-x^k)^2.

%I A163318 #13 Nov 12 2020 06:35:44
%S A163318 1,1,4,8,19,36,76,142,272,496,900,1592,2784,4792,8138,13688,22703,
%T A163318 37380,60838,98310,157298,250162,394332,618032,961512,1487563,2286610,
%U A163318 3496776,5316666,8044598,12110538,18147166,27068692,40203306,59459998,87587428,128522850
%N A163318 Expansion of g.f.: Product_{k>=1} 1+k*x^k/(1-x^k)^2.
%H A163318 Alois P. Heinz, <a href="/A163318/b163318.txt">Table of n, a(n) for n = 0..1000</a>
%p A163318 b:= proc(n,i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A163318        b(n, i-1) +add(b(n-i*j, i-1)*(j*i), j=1..n/i)))
%p A163318     end:
%p A163318 a:= n-> b(n, n):
%p A163318 seq(a(n), n=0..40);  # _Alois P. Heinz_, Feb 25 2013
%t A163318 terms = 40;
%t A163318 CoefficientList[Product[1 + k x^k/(1 - x^k)^2, {k, 1, terms}] + O[x]^terms, x] (* _Jean-François Alcover_, Nov 12 2020 *)
%Y A163318 Cf. A006906, A077285, A162506.
%K A163318 easy,nonn
%O A163318 0,3
%A A163318 _Vladeta Jovovic_, Jul 24 2009