A320753 Number of partitions of n with seven kinds of 1.

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

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