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 A361626 #17 Mar 29 2023 04:44:33
%S A361626 1,3,17,139,1437,17711,252133,4059567,72779129,1435276027,30836352441,
%T A361626 716101686323,17858449006357,475653606922599,13467411746316557,
%U A361626 403708230041927191,12767545998797849073,424670548932688771187,14814998283177691422049
%N A361626 Expansion of e.g.f. exp( x/(1-x)^3 ) / (1-x)^2.
%H A361626 Winston de Greef, <a href="/A361626/b361626.txt">Table of n, a(n) for n = 0..420</a>
%F A361626 a(n) = n! * Sum_{k=0..n} binomial(n+2*k+1,n-k)/k! = Sum_{k=0..n} (n+2*k+1)!/(3*k+1)! * binomial(n,k).
%F A361626 a(n) ~ 3^(5/8) * exp(-1/27 - 3^(3/4)*n^(1/4)/72 + sqrt(3*n)/6 + 4*3^(-3/4)*n^(3/4) - n) * n^(n + 3/8) / 6 * (1 + 63037 * 3^(1/4)/(69120 * n^(1/4))). - _Vaclav Kotesovec_, Mar 29 2023
%o A361626 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-x)^3)/(1-x)^2))
%o A361626 (PARI) a(n)=n! * sum(k=0, n, binomial(n+2*k+1,n-k)/k!) \\ _Winston de Greef_, Mar 18 2023
%Y A361626 Cf. A091695, A351767, A361599.
%Y A361626 Cf. A000262, A001339, A343884.
%K A361626 nonn
%O A361626 0,2
%A A361626 _Seiichi Manyama_, Mar 18 2023