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 A111601 #13 Aug 11 2025 14:57:45
%S A111601 1,2,9,36,225,1350,11025,88200,893025,8930250,108056025,1296672300,
%T A111601 18261468225,255660555150,4108830350625,65741285610000,
%U A111601 1187451971330625,21374135483951250,428670161650355625,8573403233007112500
%N A111601 Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).
%F A111601 E.g.f.: (1/sqrt(1-x^2))*x/(1-x).
%F A111601 a(n) = n!*Sum_{k=0..floor((n-1)/2)} binomial(2*k, k)/(4^k).
%F A111601 a(2*k+1) = A111595(2*k+2, 0)= ((2*k+1)!!)^2 = A001818(k+1), k >= 0.
%F A111601 D-finite with recurrence (-n+1)*a(n) +n*a(n-1) +n*(n-1)^2*a(n-2)=0. a(1)=1, a(2)=2. - _Sergei N. Gladkovskii_, Jul 27 2012, corrected Aug 11 2025
%Y A111601 Second column (m=1) of triangle |A111595|.
%K A111601 nonn,easy
%O A111601 1,2
%A A111601 _Wolfdieter Lang_, Aug 23 2005