A270143 - OEIS

%I #10 Mar 12 2016 10:45:53

%S 0,1,-1,3,-2,6,-3,11,-4,19,-4,31,-2,50,3,79,15,122,38,187,78,284,146,

%T 426,257,635,431,939,701,1377,1110,2007,1718,2906,2613,4178,3914,5971,

%U 5781,8482,8440,11976,12191,16816,17438,23483,24730,32615,34794,45070

%N a(n) = Sum_{k=0..n} (-1)^(k+1) * k * A000041(n-k).

%C Convolution of A000041 and A181983.

%H Vaclav Kotesovec, <a href="/A270143/b270143.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = Sum_{k=0..n} (-1)^(n-k+1) * (n-k) * A000041(k).

%F a(n) ~ A000041(n)/4.

%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (16*n*sqrt(3)).

%F G.f.: x/(1+x)^2 * Product_{k>=1} 1/(1-x^k).

%t Table[Sum[(-1)^(n-k+1)*PartitionsP[k]*(n-k), {k, 0, n}], {n, 0, 100}]

%t nmax = 100; CoefficientList[Series[x/(1 + x)^2 * Product[1/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000041, A014153, A087787, A270144.

%K sign

%O 0,4

%A _Vaclav Kotesovec_, Mar 12 2016