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A320753 Number of partitions of n with seven kinds of 1. 2
1, 7, 29, 92, 247, 590, 1292, 2644, 5124, 9494, 16939, 29262, 49156, 80577, 129252, 203363, 314462, 478683, 718339, 1064009, 1557252, 2254113, 3229631, 4583602, 6447917, 8995858, 12453830, 17116103, 23363272, 31685282, 42710057, 57238971, 76290668, 101155025 (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)^7 * 1/Product_{j>1} (1-x^j).

Euler transform of 7,1,1,1,... .

a(n) ~ 2 * 3^(5/2) * n^2 * exp(Pi*sqrt(2*n/3)) / Pi^6. - Vaclav Kotesovec, Oct 24 2018

MAPLE

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

      (numtheory[sigma](j)+6)*a(n-j), j=1..n)/n)

    end:

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

MATHEMATICA

nmax = 50; CoefficientList[Series[1/((1-x)^6 * Product[1-x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 24 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(1/((1-x)^7*prod(j=2, 40, 1-x^j))) \\ G. C. Greubel, Oct 27 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^7*(&*[1-x^j: j in [2..30]])))); // G. C. Greubel, Oct 27 2018

CROSSREFS

Column k=7 of A292508.

Sequence in context: A001779 A257201 A258475 * A053295 A266939 A055798

Adjacent sequences:  A320750 A320751 A320752 * A320754 A320755 A320756

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.)