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A270144 a(n) = Sum_{k=0..n} (-1)^(k+1) * k * A000009(n-k).

%I A270144 #9 Mar 12 2016 10:45:43
%S A270144 0,1,-1,2,-1,2,0,2,1,2,3,2,5,3,7,5,10,7,14,11,18,17,24,24,32,34,42,47,
%T A270144 56,63,74,85,96,113,126,147,165,191,213,247,275,316,353,404,449,514,
%U A270144 571,648,723,816,909,1024,1140,1278,1424,1592,1770,1976,2195,2442
%N A270144 a(n) = Sum_{k=0..n} (-1)^(k+1) * k * A000009(n-k).
%C A270144 Convolution of A000009 and A181983.
%H A270144 Vaclav Kotesovec, <a href="/A270144/b270144.txt">Table of n, a(n) for n = 0..5000</a>
%F A270144 a(n) = Sum_{k=0..n} (-1)^(n-k+1) * (n-k) * A000009(k).
%F A270144 a(n) ~ A000009(n)/4.
%F A270144 a(n) ~ exp(Pi*sqrt(n/3)) / (16*3^(1/4)*n^(3/4)).
%F A270144 G.f.: x/(1+x)^2 * Product_{k>=1} (1+x^k).
%t A270144 Table[Sum[(-1)^(n-k+1)*PartitionsQ[k]*(n-k), {k, 0, n}], {n, 0, 100}]
%t A270144 nmax = 100; CoefficientList[Series[x/(1 + x)^2 * Product[(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A270144 Cf. A000009, A025147, A095944, A270143.
%K A270144 sign
%O A270144 0,4
%A A270144 _Vaclav Kotesovec_, Mar 12 2016