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 A270922 #16 Jul 31 2025 03:47:02
%S A270922 1,1,5,28,141,751,4064,22198,122381,679375,3792155,21263331,119679000,
%T A270922 675763232,3826165838,21715370653,123502583565,703694143160,
%U A270922 4016079632039,22953901314649,131366012754691,752709483123304,4317601694413683,24790635783551008
%N A270922 Coefficient of x^n in Product_{k>=1} (1 + x^k)^(k*n).
%C A270922 From _Peter Bala_, Apr 18 2023: (Start)
%C A270922 The Gauss congruences a(n*p^k) == a(n*p^(k-1)) (mod p^k) hold for all primes p and all positive integers n and k.
%C A270922 Conjecture: the stronger supercongruences a(n*p^k) == a(n*p^(k-1)) (mod p^(2*k)) hold for all primes p >= 3 and all positive integers n and k. (End)
%H A270922 Vaclav Kotesovec, <a href="/A270922/b270922.txt">Table of n, a(n) for n = 0..500</a>
%F A270922 a(n) ~ c * d^n / sqrt(n), where d = 5.86811560195778704624328861800917668... and c = 0.25351514412215050116013727161633502...
%F A270922 a(n) = [x^n] exp(n*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 30 2018
%t A270922 Table[SeriesCoefficient[Product[(1+x^k)^(k*n), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
%Y A270922 Cf. A255672, A270913, A270917, A270924, A380291.
%K A270922 nonn
%O A270922 0,3
%A A270922 _Vaclav Kotesovec_, Mar 26 2016