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%I #12 Jan 07 2015 07:08:04
%S 1,0,1,2,1,1,0,3,2,1,4,3,5,3,1,0,7,8,8,4,1,8,7,15,16,12,5,1,0,15,22,
%T 31,28,17,6,1,16,15,37,53,59,45,23,7,1,0,31,52,90,112,104,68,30,8,1,
%U 32,31,83,142,202,216,172,98,38,9,1,0,63,114,225
%N Riordan array (1/(1-2*x^2), x/(1-x)).
%C Row sums are A007179(n+1).
%F T(n,n)=1, T(2n,0)=2^n, T(2n+1,0)=0, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0<k<n.
%F T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k)-T(n-3,k)-2*T(n-3,k-1), T(0,0)=1, T(1,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n.
%F T(n,n)=1, T(n+1,n)=n, T(n+2,n)=n*(n+1)/2 + 2.
%F exp(x) * e.g.f. for row n = e.g.f. for diagonal n. For example, for n = 3 we have exp(x)*(3*x + 2*x^2/2! + x^3/3!) = 3*x + 8*x^2/2! + 16*x^3/3! + 28*x^4/4! + 45*x^5/5! + .... The same property holds more generally for Riordan arrays of the form ( f(x), x/(1 - x) ). - _Peter Bala_, Dec 22 2014
%e Triangle begins (0<=k<=n):
%e 1
%e 0, 1
%e 2, 1, 1
%e 0, 3, 2, 1
%e 4, 3, 5, 3, 1
%e 0, 7, 8, 8, 4, 1
%e 8, 7, 15, 16, 12, 5, 1
%e 0, 15, 22, 31, 28, 17, 6, 1
%Y Cf. Columns: A077957, A052551, A077866.
%Y Diagonals: A000012, A001477, A022856.
%Y Cf. Similar sequences: A059260, A191582.
%K nonn,easy,tabl
%O 0,4
%A _Philippe Deléham_, Jan 11 2014
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