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A278407 G.f.: x^2 * f''(x), where f(x) = Product_{k>=1} (1 + x^k).

%I A278407 #6 Nov 22 2016 17:10:40
%S A278407 0,0,2,12,24,60,120,210,336,576,900,1320,1980,2808,4004,5670,7680,
%T A278407 10336,14076,18468,24320,31920,41118,52624,67344,85200,107250,134784,
%U A278407 167832,207872,257520,316200,386880,473088,574464,696150,841680,1012320,1214784,1455324
%N A278407 G.f.: x^2 * f''(x), where f(x) = Product_{k>=1} (1 + x^k).
%H A278407 Robert Israel, <a href="/A278407/b278407.txt">Table of n, a(n) for n = 0..10000</a>
%F A278407 a(n) = n*(n-1)*A000009(n).
%p A278407 g:= mul(1+x^k,k=1..100):
%p A278407 S1:= series(g,x,101):
%p A278407 S2:= series(x^2*diff(S1,x$2),x,101):
%p A278407 seq(coeff(S2,x,j),j=0..100); # _Robert Israel_, Nov 22 2016
%t A278407 nmax=60; CoefficientList[Series[x^2*D[Product[1+x^k, {k, 1, nmax}], {x, 2}], {x, 0, nmax}], x]
%t A278407 nmax=60; CoefficientList[Series[Product[1+x^k, {k, 1, nmax}], {x, 0, nmax}], x]*Range[0, nmax]*(Range[0, nmax]-1)
%Y A278407 Cf. A000009, A066189, A278406.
%K A278407 nonn
%O A278407 0,3
%A A278407 _Vaclav Kotesovec_, Nov 21 2016