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Diagonal sums of number triangle A112292.
1

%I #3 Mar 30 2012 18:59:12

%S 1,1,4,18,121,1055,11376,145852,2165689,36532197,689873284,

%T 14415662558,330204013569,8226714806323,221470234531456,

%U 6406397898751320,198160750081637521,6526636388676159977,228040136335670652324

%N Diagonal sums of number triangle A112292.

%F a(n)=sum{k=0..floor(n/2), (2n-2k-1)!!/(2k-1)!!}; a(n)=sum{k=0..floor(n/2), 2^(n-2k)(n-k-1/2)!/(k-1/2)!}; a(n)=sum{k=0..floor(n/2), (n-k)!C(2n-2k, n-k)2^(2k-n)/(k!C(2k, k))}; a(n)=sum{k=0..floor(n/2), (n-k+1)!*C(n-k)2^(2k-n)/((k+1)!*C(k))}.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Sep 01 2005