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

0,2

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

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

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 *)

Crossrefs

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

Column k=6 of A292508.

Sequence in context: A307621 A257200 A258474 * A053739 A280481 A055797

Adjacent sequences: A120474 A120475 A120476 * A120478 A120479 A120480

Keyword

nonn

Author

Jonathan Vos Post, Jul 21 2006

Extensions

More terms from Emeric Deutsch, Jul 24 2006

Status

approved