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 A316144 #21 Feb 28 2024 10:47:57
%S A316144 1,4,28,268,3148,43564,692428,12390508,245896588,5351817004,
%T A316144 126614238028,3232332423148,88500275727628,2585371577628844,
%U A316144 80227707005300428,2634361286274638188,91223969834203056268,3321457538305952791084,126817592900018186967628
%N A316144 Expansion of e.g.f. Product_{k>=1} ((1 + (exp(x)-1)^k) / (1 - (exp(x)-1)^k))^2.
%C A316144 Self-convolution of A306045.
%C A316144 Convolution of A316142 and A316143.
%C A316144 Conjecture: Let k be a positive integer. The sequence obtained by reducing a(n) modulo k is eventually periodic with the period dividing phi(k) = A000010(k). For example, modulo 7 we obtain the sequence [1, 4, 0, 2, 5, 3, 2, 4, 0, 2, 5, 3, 2, 4, 0, 2, 5, 3, 2, ...], with a preperiod of length 1 and an apparent period thereafter of 6 = phi(7). - _Peter Bala_, Mar 03 2023
%H A316144 Vaclav Kotesovec, <a href="/A316144/b316144.txt">Table of n, a(n) for n = 0..400</a>
%F A316144 Sum_{k=0..n} binomial(n,k) * A306045(k) * A306045(n-k).
%F A316144 a(n) ~ n! * exp(Pi * sqrt(n/log(2)) - Pi^2 * (1 - 1/log(2)) / 8) / (2^(7/2) * n^(5/4) * log(2)^(n - 1/4)).
%t A316144 nmax = 20; CoefficientList[Series[Product[((1+(Exp[x]-1)^k)/(1-(Exp[x]-1)^k))^2, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
%Y A316144 Cf. A001934, A306045, A316142, A316143.
%K A316144 nonn,easy
%O A316144 0,2
%A A316144 _Vaclav Kotesovec_, Jun 25 2018