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 A283271 #20 Jan 29 2025 22:30:39
%S A283271 1,-1,-16,-65,-55,807,4809,13135,550,-169070,-862710,-2281174,
%T A283271 -1221309,20194565,114391575,346400092,486546751,-1239516671,
%U A283271 -11089537215,-41702958960,-93143227027,-45337210750,674845109986,3682196642725,11405949184465,20796945542222
%N A283271 Expansion of exp( Sum_{n>=1} -sigma_5(n)*x^n/n ) in powers of x.
%C A283271 Let A(x) denote the g.f. and let m be an integer. Define a sequence by u(n) = [x^n] A(x)^(m*n). We conjecture that the supercongruence u(n*p^r) == u(n*p^(r-1)) (mod p^(3*r)) holds for all positive integers n and r and all primes p >= 7. Cf. A380581. - _Peter Bala_, Jan 21 2025
%H A283271 Seiichi Manyama, <a href="/A283271/b283271.txt">Table of n, a(n) for n = 0..1000</a>
%F A283271 G.f.: Product_{n>=1} (1 - x^n)^(n^4).
%F A283271 a(n) = -(1/n)*Sum_{k=1..n} sigma_5(k)*a(n-k).
%Y A283271 Column k=4 of A283272.
%Y A283271 Cf. A023873 (exp( Sum_{n>=1} sigma_5(n)*x^n/n )).
%Y A283271 Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), A283263 (k=3), A283264 (k=4), this sequence (k=5).
%K A283271 sign
%O A283271 0,3
%A A283271 _Seiichi Manyama_, Mar 04 2017