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A193450 Triangle of a binomial convolution sum related to Jacobsthal numbers.

%I A193450 #14 Jun 04 2014 15:12:55
%S A193450 0,1,0,2,2,2,3,6,6,0,4,12,16,8,4,5,20,35,30,15,0,6,30,66,78,54,18,6,7,
%T A193450 42,112,168,154,84,28,0,8,56,176,320,368,272,128,32,8,9,72,261,558,
%U A193450 774,720,450,180,45,0,10,90,370,910,1480,1660,1300,700,250,50,10
%N A193450 Triangle of a binomial convolution sum related to Jacobsthal numbers.
%C A193450 Row sum is A193449(n) = A001045(n+1)*n.
%F A193450 T(n,k) = sum( (-1)^j*n*C(n-j,k-j), j=0..k).
%F A193450 T(n,k) = n*C(n, k)*2F1( (1, -k); -n )(-1).
%e A193450 Triangle starts:
%e A193450 0;
%e A193450 1, 0;
%e A193450 2, 2, 2;
%e A193450 3, 6, 6, 0;
%e A193450 4, 12, 16, 8, 4;
%e A193450 5, 20, 35, 30, 15, 0;
%e A193450 ...
%o A193450 (PARI) T(n,k) = sum(j=0, k, (-1)^j*n*binomial(n-j,k-j)); \\ _Michel Marcus_, Jun 04 2014
%Y A193450 Cf. A193451.
%K A193450 nonn,easy,tabl
%O A193450 0,4
%A A193450 _Olivier Gérard_, Jul 26 2011