A291590 Column 5 of A060244.

0, 0, 0, 0, 2, 5, 11, 22, 40, 70, 116, 187, 292, 448, 670, 988, 1432, 2051, 2896, 4052, 5603, 7687, 10446, 14096, 18870, 25108, 33176, 43601, 56960, 74051, 95762, 123300, 158011, 201692, 256368, 324682, 409642, 515116, 645509, 806430, 1004292, 1247146, 1544237

Offset

1,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

G.f.: x^5 * (2 + 3*x + 2*x^2 + x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 2*x^7 + 2*x^9 + 2*x^10 + x^11 - x^13)/((1 - x)^4 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)) * Product_{k>=1} 1/(1 - x^k).

a(n) ~ sqrt(3) * n * exp(Pi*sqrt(2*n/3)) / (40*Pi^4).

a(n) ~ 3*n^2 * A000041(n) / (10*Pi^4).

Mathematica

nmax = 30; col = 5; Flatten[{0, 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^5*(2 + 3*x + 2*x^2 + x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 2*x^7 + 2*x^9 + 2*x^10 + x^11 - x^13)/((1 - x)^4 * (1 + x)^2 * (1 + x^2) * (1 + x + x^2) * (1 + x + x^2 + x^3 + x^4)) / QPochhammer[x], {x, 0, 100}], x]]
Table[Sum[(1 + (k-4)*(645 + 10*k + k^2)/720 - Floor[(k-4)/5]/5 - Floor[(k-4)/4]/4 + (k+1)*Floor[(k-4)/2]/8 - Floor[(k-3)/5]/5 - Floor[(k-3)/4]/4 - Floor[(k-3)/3]/3 - 3*Floor[(k-1)/5]/5) * PartitionsP[n-k], {k, 5, n}], {n, 1, 100}]

Crossrefs

Cf. A060244.

Sequence in context: A292528 A135119 A290778 * A236430 A058696 A134508

Adjacent sequences: A291587 A291588 A291589 * A291591 A291592 A291593

Keyword

nonn

Author

Vaclav Kotesovec, Aug 27 2017

Status

approved