This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A237512 #27 Sep 02 2018 02:07:22
%S A237512 0,1,0,1,47,55496,2080571733,4441900888487987,
%T A237512 849835826032526606030103,20540228659655619974131131927286681,
%U A237512 82853643094578125257400348993596774353069331199,70898139566455107685443806945119782661588205935442233026505921
%N A237512 Number of solutions to Sum_{k=1..n} k*c(k) = n! , c(k) > 0.
%C A237512 a(n) is the number of partitions of n! - n*(n+1)/2 into parts that are at most n. - _Alois P. Heinz_, Feb 08 2014
%H A237512 Alois P. Heinz, <a href="/A237512/b237512.txt">Table of n, a(n) for n = 0..31</a>
%H A237512 A. V. Sills and D. Zeilberger, <a href="http://arxiv.org/abs/1108.4391">Formulae for the number of partitions of n into at most m parts (using the quasi-polynomial ansatz)</a> (arXiv:1108.4391 [math.CO])
%H A237512 StackExchange, <a href="http://math.stackexchange.com/questions/655541">Combinations sum_{k=1..m} k*n_k = m!</a>, Jan 29 2014
%F A237512 a(n) = [x^(n!)] Product_{k=1..n} x^k/(1-x^k).
%F A237512 a(n) = [x^(n!-n*(n+1)/2)] Product_{k=1..n} 1/(1-x^k). - _Alois P. Heinz_, Feb 08 2014
%F A237512 a(n) ~ n * (n!)^(n-3) ~ n^(n^2-5*n/2-1/2) * (2*Pi)^((n-3)/2) / exp(n*(n-3)-1/12). - _Vaclav Kotesovec_, Jun 05 2015
%t A237512 Table[Coefficient[Series[Product[x^k/(1-x^k),{k,n}],{x,0,n!}],x^(n!) ] ,{n,7}]
%Y A237512 Cf. A236810.
%K A237512 nonn
%O A237512 0,5
%A A237512 _Wouter Meeussen_, Feb 08 2014
%E A237512 a(8)-a(11) from _Alois P. Heinz_, Feb 08 2014