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

0,2

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

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

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 *)

Crossrefs

Cf. A000041.

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

Column k=5 of A292508.

Sequence in context: A078449 A257199 A258473 * A014166 A014171 A014175

Adjacent sequences: A014158 A014159 A014160 * A014162 A014163 A014164

Keyword

nonn

Author

N. J. A. Sloane

Status

approved