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A258672 Number of partitions of n*2^n into parts that are at most n. 3
0, 1, 5, 61, 2280, 273052, 110537709, 156456474138, 790541795804221, 14445283925963101577, 963056085414756870071490, 235864774408401842540220265704, 213426797830699546133563821747980513, 717147073290996884137625501875655000693923 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: If f(n) >= O(n^4) then "number of partitions of f(n) into parts that are at most n" is asymptotic to f(n)^(n-1) / (n!*(n-1)!). For the examples see A238016 and A238010.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..59

A. V. Sills and D. Zeilberger, Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz) (arXiv:1108.4391 [math.CO])

FORMULA

a(n) ~ n^n * 2^(n*(n-1)) / (n!)^2.

CROSSREFS

Cf. A236810, A237998, A238000, A238010, A238016.

Sequence in context: A028296 A159316 A231798 * A201254 A116163 A092823

Adjacent sequences:  A258669 A258670 A258671 * A258673 A258674 A258675

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 07 2015

STATUS

approved

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Last modified October 22 14:46 EDT 2018. Contains 316487 sequences. (Running on oeis4.)