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 A303914 #8 May 04 2018 06:45:18
%S A303914 1,2,9,55,465,5051,69265,1147287,22307905,497211049,12484203601,
%T A303914 348391613615,10691846920081,357749800027465,12958472141161457,
%U A303914 505088781523073326,21076091000708067585,937322034938743608556,44256147057318887809993,2210813717869831566759857,116492226446226314836976401
%N A303914 a(n) = [x^n] (1/(1 - x))*Product_{k>=1} 1/(1 - n*x^k).
%H A303914 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A303914 a(n) = [x^n] (1/(1 - x))*exp(Sum_{k>=1} n^k*x^k/(k*(1 - x^k))).
%F A303914 a(n) = Sum_{j=0..n} A246935(j,n).
%F A303914 a(n) ~ n^n. - _Vaclav Kotesovec_, May 04 2018
%p A303914 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A303914 b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
%p A303914 end:
%p A303914 a:= n-> add(b(j$2, n), j=0..n):
%p A303914 seq(a(n), n=0..20); # _Alois P. Heinz_, May 02 2018
%t A303914 Table[SeriesCoefficient[1/(1 - x) Product[1/(1 - n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
%t A303914 Table[SeriesCoefficient[1/(1 - x) Exp[Sum[n^k x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 20}]
%Y A303914 Cf. A000070, A124577, A246935, A303070.
%K A303914 nonn
%O A303914 0,2
%A A303914 _Ilya Gutkovskiy_, May 02 2018