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%I #6 Oct 08 2016 12:07:03
%S 1,1,7,32,283,2643,32317,443824,7115461,127222805,2541399091,
%T 55739417376,1335729425647,34666455314407,969419191792633,
%U 29046504524166368,928541094344685577,31540972026299055849
%N Diagonal sums of a number triangle related to the Jacobsthal numbers.
%C Diagonal sums of number triangle A110321.
%F a(n)=sum{k=0..floor(n/2), (n-k)!*J(n-2k+1)/k!}, J(n)=A001045(n).
%t J[n_] := (2^n-(-1)^n)/3; a[n_] := Sum[(n-k)!*J[n-2*k+1]/k!, {k, 0, n/2}]; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Oct 08 2016 *)
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jul 20 2005