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 A163843 #13 Aug 22 2025 04:25:17
%S A163843 1,3,10,41,116,427,1240,4181,12472,40091,121364,380701,1160186,
%T A163843 3593969,10979532,33785469,103258800,316532947,966976444,2957131673,
%U A163843 9026437602,27558146133,84043120308,256263107177,780817641926
%N A163843 Row sums of triangle A163840.
%H A163843 G. C. Greubel, <a href="/A163843/b163843.txt">Table of n, a(n) for n = 0..1000</a>
%H A163843 Peter Luschny, <a href="http://www.luschny.de/math/swing/SwingingFactorial.html">Swinging Factorial</a>.
%F A163843 a(n) = Sum_{k=0..n} Sum_{i=k..n} binomial(n-k,n-i)*i$ where i$ denotes the swinging factorial of i (A056040).
%p A163843 swing := proc(n) option remember; if n = 0 then 1 elif
%p A163843 irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
%p A163843 a := proc(n) local i,k; add(add(binomial(n-k,n-i)*swing(i),i=k..n),k=0..n) end:
%t A163843 sf[n_] := n!/Quotient[n, 2]!^2; t[n_, k_] := Sum[Binomial[n - k, n - i]*sf[i], {i, k, n}]; Table[Sum[t[n, k], {k, 0, n}], {n, 0, 50}] (* _G. C. Greubel_, Aug 06 2017 *)
%Y A163843 Cf. A056040, A163840.
%K A163843 nonn,changed
%O A163843 0,2
%A A163843 _Peter Luschny_, Aug 06 2009