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A320754 Number of partitions of n with eight kinds of 1. 2
1, 8, 37, 129, 376, 966, 2258, 4902, 10026, 19520, 36459, 65721, 114877, 195454, 324706, 528069, 842531, 1321214, 2039553, 3103562, 4660814, 6914927, 10144558, 14728160, 21176077, 30171935, 42625765, 59741868, 83105140, 114790422, 157500479, 214739450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: 1/(1-x)^8 * 1/Product_{j>1} (1-x^j).

Euler transform of 8,1,1,1,... .

a(n) ~ 2^(3/2) * 3^3 * n^(5/2) * exp(Pi*sqrt(2*n/3)) / Pi^7. - Vaclav Kotesovec, Oct 24 2018

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      (numtheory[sigma](j)+7)*a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..40);

MATHEMATICA

nmax = 50; CoefficientList[Series[1/((1-x)^7 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 24 2018 *)

PROG

(PARI) x='x+O('x^40); Vec(1/((1-x)^8*prod(j=2, 40, 1-x^j))) \\ G. C. Greubel, Oct 27 2018

(MAGMA) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^8*(&*[1-x^j: j in [2..30]])))); // G. C. Greubel, Oct 27 2018

CROSSREFS

Column k=8 of A292508.

Sequence in context: A052387 A001780 A258476 * A053296 A055799 A035038

Adjacent sequences:  A320751 A320752 A320753 * A320755 A320756 A320757

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 20 2018

STATUS

approved

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Last modified September 23 12:11 EDT 2021. Contains 347617 sequences. (Running on oeis4.)