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 A344399 #10 Sep 07 2025 02:10:04
%S A344399 1,4,30,200,1190,6552,34188,171600,836550,3986840,18660356,86062704,
%T A344399 392102620,1768102000,7902970200,35056559520,154477660230,
%U A344399 676745803800,2949418972500,12794985495600,55276458056820,237909980502480,1020487997404200,4363718285628000
%N A344399 a(n) = 4^n*binomial(n - 1/2, -1/2)*(n^2 + 1).
%F A344399 a(n) = [x^n] (20*x^2 - 6*x + 1) / (1 - 4*x)^(5/2).
%F A344399 a(n) = a(n-1)*(-2 + 4*n - 2*n^2 + 4*n^3) / (2*n - 2*n^2 + n^3) for n > 0.
%F A344399 a(n) ~ 4^n * n^(3/2) / sqrt(Pi). - _Amiram Eldar_, Sep 07 2025
%p A344399 aList := proc(len) local gf, ser;
%p A344399 gf := (20*x^2 - 6*x + 1) / (1 - 4*x)^(5/2): ser := series(gf, x, len+2):
%p A344399 seq(coeff(ser, x, n), n = 0..len) end: aList(23);
%t A344399 Table[4^n Binomial[n-1/2,-1/2](n^2+1),{n,0,30}] (* _Harvey P. Dale_, Jun 20 2021 *)
%Y A344399 Cf. A344400, A344401.
%K A344399 nonn,changed
%O A344399 0,2
%A A344399 _Peter Luschny_, May 17 2021