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%I #2 Mar 30 2012 17:27:12
%S 1,13,109,765,4881,29369,169919,956237,5272945,28632525,153638211,
%T 816715073,4309138419,22598433555,117926579385,612863125965,
%U 3174156512865
%N Row sums of triangle A163842.
%C a(n) = sum{k=0..n} sum{i=k..n} binomial(n-k,n-i)*(2i+1)$
%C where i$ denotes the swinging factorial of i (A056040).
%H Peter Luschny, <a href="http://www.luschny.de/math/swing/SwingingFactorial.html"> Swinging Factorial</a>.
%p swing := proc(n) option remember; if n = 0 then 1 elif
%p irem(n, 2) = 1 then swing(n-1)*n else 4*swing(n-1)/n fi end:
%p a := proc(n) local i,k; add(add(binomial(n-k,n-i)*swing(2*i+1),i=k..n),k=0..n) end:
%Y Cf. A163842.
%K nonn
%O 0,2
%A _Peter Luschny_, Aug 06 2009
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