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A120477 Apply partial sum operator 5 times to partition numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 28 15:04 EDT 2022. Contains 354115 sequences. (Running on oeis4.)