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 A384167 #11 May 21 2025 06:38:33
%S A384167 1,10,143,2736,66009,1926912,66086271,2605455360,116123049585,
%T A384167 5774107852800,316921177332495,19032668386099200,1241454631056114825,
%U A384167 87402945316493721600,6606130538582006306175,533534147838972474163200,45855293972076668267481825,4178822478568980876361728000
%N A384167 a(n) = 2^n * n! * binomial(3*n/2,n) * Sum_{k=1..n} 1/(n+2*k).
%F A384167 a(n) = Sum_{k=0..n} k * (n+2)^(k-1) * 2^(n-k) * |Stirling1(n,k)|.
%F A384167 a(n) = n! * [x^n] ( -log(1 - 2*x)/(2 * (1 - 2*x)^(n/2+1)) ).
%o A384167 (PARI) a(n) = sum(k=0, n, k*(n+2)^(k-1)*2^(n-k)*abs(stirling(n, k, 1)));
%Y A384167 Cf. A098118, A384168, A384169.
%Y A384167 Cf. A113551.
%K A384167 nonn
%O A384167 1,2
%A A384167 _Seiichi Manyama_, May 21 2025