A291589 Column 4 of A060244.

0, 0, 0, 2, 3, 8, 13, 26, 40, 69, 104, 165, 241, 363, 517, 750, 1046, 1473, 2018, 2779, 3746, 5063, 6733, 8959, 11769, 15454, 20082, 26068, 33549, 43108, 54997, 70037, 88645, 111979, 140714, 176462, 220280, 274418, 340480, 421593, 520154, 640481, 786104, 962976

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

Cf. A060244.

Sequence in context: A262021 A221181 A116503 * A105204 A352603 A318621

Adjacent sequences: A291586 A291587 A291588 * A291590 A291591 A291592

Keyword

nonn

Author

Vaclav Kotesovec, Aug 27 2017

Status

approved