A239162 Number of partitions of 3^n into parts that are at most n with at least one part of each size.

0, 1, 4, 48, 3042, 1067474, 2215932130, 29012104252380, 2526293243761311036, 1525710603023191548743988, 6600334932211428773703751221040, 209705652574790086852527310591449309624, 49907101066058865036206450041083799915221352487

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..49

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], 2011.

Formula

a(n) = [x^(3^n-n*(n+1)/2)] Product_{j=1..n} 1/(1-x^j).

a(n) ~ 3^(n*(n-1)) / (n!*(n-1)!). - Vaclav Kotesovec, Jun 05 2015

Example

a(2) = 4: 22221, 222111, 2211111, 21111111.

Mathematica

maxExponent = 30; 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[3^n - n(n+1)/2 + 1] // Round]; Table[an = a[n];
Print[n, " ", an]; an, {n, 0, 12}] (* Jean-François Alcover, Nov 15 2018 *)

Crossrefs

Column k=3 of A238012.

Sequence in context: A197927 A100568 A112693 * A136384 A123373 A264265

Adjacent sequences: A239159 A239160 A239161 * A239163 A239164 A239165

Keyword

nonn

Author

Alois P. Heinz, Mar 11 2014

Status

approved