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

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, 56, 63, 74, 85, 96, 113, 126, 147, 165, 191, 213, 247, 275, 316, 353, 404, 449, 514, 571, 648, 723, 816, 909, 1024, 1140, 1278, 1424, 1592, 1770, 1976, 2195, 2442

Offset: 0

Author

Vaclav Kotesovec, Mar 12 2016

Keywords

• sign

Comments

Convolution of A000009 and A181983.

Links

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

Crossrefs

Cf. A000009, A025147, A095944, A270143.

Programs

Mathematica

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

Formula

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

a(n) ~ A000009(n)/4.

a(n) ~ exp(Pi*sqrt(n/3)) / (16*3^(1/4)*n^(3/4)).

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