A270143 a(n) = Sum_{k=0..n} (-1)^(k+1) * k * A000041(n-k).

0, 1, -1, 3, -2, 6, -3, 11, -4, 19, -4, 31, -2, 50, 3, 79, 15, 122, 38, 187, 78, 284, 146, 426, 257, 635, 431, 939, 701, 1377, 1110, 2007, 1718, 2906, 2613, 4178, 3914, 5971, 5781, 8482, 8440, 11976, 12191, 16816, 17438, 23483, 24730, 32615, 34794, 45070

Offset: 0

Author

Vaclav Kotesovec, Mar 12 2016

Keywords

• sign

Comments

Convolution of A000041 and A181983.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000041, A014153, A087787, A270144.

Programs

Mathematica

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

Formula

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

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

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

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