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Triangle of a binomial convolution sum related to Jacobsthal numbers.
2

%I #14 Jun 04 2014 15:12:55

%S 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 42,112,168,154,84,28,0,8,56,176,320,368,272,128,32,8,9,72,261,558,

%U 774,720,450,180,45,0,10,90,370,910,1480,1660,1300,700,250,50,10

%N Triangle of a binomial convolution sum related to Jacobsthal numbers.

%C Row sum is A193449(n) = A001045(n+1)*n.

%F T(n,k) = sum( (-1)^j*n*C(n-j,k-j), j=0..k).

%F T(n,k) = n*C(n, k)*2F1( (1, -k); -n )(-1).

%e Triangle starts:

%e 0;

%e 1, 0;

%e 2, 2, 2;

%e 3, 6, 6, 0;

%e 4, 12, 16, 8, 4;

%e 5, 20, 35, 30, 15, 0;

%e ...

%o (PARI) T(n,k) = sum(j=0, k, (-1)^j*n*binomial(n-j,k-j)); \\ _Michel Marcus_, Jun 04 2014

%Y Cf. A193451.

%K nonn,easy,tabl

%O 0,4

%A _Olivier GĂ©rard_, Jul 26 2011