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Riordan array (1,2+3x).
0

%I #5 Feb 19 2015 15:09:12

%S 1,0,2,0,3,4,0,0,12,8,0,0,9,36,16,0,0,0,54,96,32,0,0,0,27,216,240,64,

%T 0,0,0,0,216,720,576,128,0,0,0,0,81,1080,2160,1344,256,0,0,0,0,0,810,

%U 4320,6048,3072,512,0,0,0,0,0,243,4860,15120,16128,6912,1024,0,0,0,0,0,0

%N Riordan array (1,2+3x).

%C Row sums are A015518(n+1). Diagonal sums are A002447. The Riordan array (1,s+tx) defines T(n,k)=binomial(k,n-k)s^k(t/s)^(n-k). The row sums satisfy a(n)=s*a(n-1)+t*a(n-2) and the diagonal sums satisfy a(n)=s*a(n-2)+t*a(n-3).

%F Number triangle T(n, k)=binomial(k, n-k)2^k*(3/2)^(n-k) Columns have g.f. (2x+3x^2)^k.

%e Rows begin

%e 1;

%e 0,2;

%e 0,3,4;

%e 0,0,12,8;

%e 0,0,9,36,16;

%K easy,nonn,tabl

%O 0,3

%A _Paul Barry_, Sep 25 2004