A120477 Apply partial sum operator 5 times to partition numbers.

1, 6, 22, 63, 155, 343, 702, 1352, 2480, 4370, 7445, 12323, 19894, 31421, 48675, 74111, 111099, 164221, 239656, 345670, 493243, 696861, 975518, 1353971, 1864315, 2547941, 3457972, 4662273, 6247169, 8322010, 11024775, 14528914, 19051697

Offset: 0

Author

Jonathan Vos Post, Jul 21 2006

Keywords

• nonn

Comments

In general, if g.f. = 1/(1-x)^m * Product_{k>=1} 1/(1-x^k), then a(n) ~ 2^(m/2 - 2) * 3^((m-1)/2) * n^(m/2 - 1) * exp(Pi*sqrt(2*n/3)) / Pi^m. - Vaclav Kotesovec, Oct 30 2015

Links

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

Crossrefs

Cf. A000041, A000070, A014153, A014160, A014161.

Column k=6 of A292508.

Programs

Maple

with(combinat): g:=1/(1-x)^5/product(1-x^k,k=1..50): gser:=series(g,x=0,40): seq(coeff(gser,x,n),n=0..37); # Emeric Deutsch, Jul 24 2006

Mathematica

nmax = 50; CoefficientList[Series[1/((1-x)^5 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 30 2015 *)

Formula

G.f.: 1/((1-x)^5*Product_{k>=1} (1-x^k)). - Emeric Deutsch, Jul 24 2006

a(n) ~ 9*sqrt(2)*n^(3/2) * exp(Pi*sqrt(2*n/3)) / Pi^5. - Vaclav Kotesovec, Oct 30 2015

Extensions

More terms from Emeric Deutsch, Jul 24 2006