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 A293528 #20 Mar 29 2022 03:41:20
%S A293528 1,1,3,13,97,741,7291,81313,1027713,14231017,220911571,3730744821,
%T A293528 68096325793,1339705629133,28225576881867,634123159354441,
%U A293528 15127595174135041,381586517104288593,10147599723510322723,283846981316172613597,8324822922497497733601
%N A293528 E.g.f.: exp(x * Product_{k>0} (1 + x^k)).
%C A293528 From _Peter Bala_, Mar 28 2022: (Start)
%C A293528 The congruence a(n+k) == a(n) (mod k) holds for all n and k.
%C A293528 It follows that the sequence obtained by taking a(n) modulo a fixed positive integer k is periodic with exact period dividing k. For example, the sequence taken modulo 10 becomes [1, 1, 3, 3, 7, 1, 1, 3, 3, 7, ...], a purely periodic sequence with period 5.
%C A293528 3 divides a(3*n+2); 13 divides a(13*n+3) and a(13*n+5); 19 divides a(19*n+5), a(19*n+12) and a(19*n+14). (End)
%H A293528 Seiichi Manyama, <a href="/A293528/b293528.txt">Table of n, a(n) for n = 0..431</a>
%H A293528 Peter Bala, <a href="/A047974/a047974_1.pdf">Integer sequences that become periodic on reduction modulo k for all k</a>
%F A293528 a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} k*A000009(k-1)*a(n-k)/(n-k)! for n > 0.
%t A293528 nmax = 25; CoefficientList[Series[E^(x*QPochhammer[-1, x]/2), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 11 2017 *)
%o A293528 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x*prod(k=1, N, (1+x^k)))))
%Y A293528 Cf. A000009, A293527, A293840.
%K A293528 nonn,easy
%O A293528 0,3
%A A293528 _Seiichi Manyama_, Oct 11 2017