A014161 Apply partial sum operator 4 times to partition numbers.

1, 5, 16, 41, 92, 188, 359, 650, 1128, 1890, 3075, 4878, 7571, 11527, 17254, 25436, 36988, 53122, 75435, 106014, 147573, 203618, 278657, 378453, 510344, 683626, 910031, 1204301, 1584896, 2074841, 2702765

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

A014161 convolved with A010815 = the tetrahedral numbers: 1, 4, 10, 20, 35, ... . - Gary W. Adamson, Nov 09 2008

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041.

Cf. A010815. - Gary W. Adamson, Nov 09 2008

Column k=5 of A292508.

Programs

Mathematica

nmax = 50; CoefficientList[Series[1/((1-x)^4 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *)

Formula

a(n) ~ 3^(3/2)*n * exp(Pi*sqrt(2*n/3)) / Pi^4. - Vaclav Kotesovec, Oct 30 2015

G.f.: 1/(1-x)^4 * Product_{k>=1} 1/(1-x^k). - Vaclav Kotesovec, Oct 30 2015