OFFSET
1,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: x^4 * (2 + x + x^2 - x^3 - x^4 - x^5 - x^6 + x^7) / ((1 - x)^3 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2)) * Product_{k>=1} 1/(1 - x^k).
a(n) ~ exp(Pi*sqrt(2*n/3)) * sqrt(n) / (8*sqrt(2)*Pi^3).
a(n) ~ sqrt(3) * n^(3/2) * A000041(n) / (2^(3/2) * Pi^3).
MATHEMATICA
nmax = 50; col = 4; Flatten[{0, 0, 0, CoefficientList[Coefficient[Normal[Series[Product[Product[1/(1 - x^(i - j)*y^j), {j, 0, i}], {i, 2, nmax + col}], {x, 0, col}, {y, 0, nmax}]], x^col], y]}]
Rest[CoefficientList[Series[x^4*(2 + x + x^2 - x^3 - x^4 - x^5 - x^6 + x^7) / ((1 - x)^3 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2)) / QPochhammer[x], {x, 0, 100}], x]]
Table[Sum[(7*k^2/48 + 47*(k-4)/48 + Floor[(k-3)/4]/2 - (2*k + 19)*Floor[(k-3)/2]/8 + Floor[(k-2)/3]/3 - Floor[k/3]/3) * PartitionsP[n-k], {k, 4, n}], {n, 1, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 27 2017
STATUS
approved