A239165 - OEIS

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A239165

Number of partitions of 6^n into parts that are at most n with at least one part of each size.

0, 1, 17, 3781, 14942231, 1264608203048, 2555847904495965819, 132574244496779071303074376, 185560862224740635595130202984468935, 7271076505438083132065943012753686950455454055, 8205115354631567886718289443554629632451344416164686337673 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	LINKS	`Alois P. Heinz, Table of n, a(n) for n = 0..37` `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) = [x^(6^n-n(n+1)/2)] Product_{j=1..n} 1/(1-x^j).` `a(n) ~ 6^(n(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015`
	MATHEMATICA	`maxExponent = 50; a[0] = 0; a[1] = 1;` `a[n_] := Module[{}, aparts = List @@ (Product[1/(1 - x^j), {j, 1, n}] // Apart); cc = aparts + O[x]^maxExponent // CoefficientList[#, x]&; f[k_] = Total[FindSequenceFunction[#, k]& /@ cc]; f[6^n-n(n+1)/2+1] // Round];` `Table[an = a[n]; Print[n, " ", an]; an, {n, 0, 10}] (* Jean-François Alcover, Nov 15 2018 *)`
	CROSSREFS	`Column k=6 of A238012.` `Sequence in context: A125000 A228195 A032909 * A329168 A194015 A015058` `Adjacent sequences: A239162 A239163 A239164 * A239166 A239167 A239168`
	KEYWORD	`nonn`
	AUTHOR	`Alois P. Heinz, Mar 11 2014`
	STATUS	`approved`

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)