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%I #2 Mar 30 2012 18:59:25
%S 1,1,1,1,3,1,1,6,6,1,1,10,20,10,1,1,15,50,50,15,1,1,21,105,176,105,21,
%T 1,1,28,196,497,497,196,28,1,1,36,336,1204,1830,1204,336,36,1,1,45,
%U 540,2604,5634,5634,2604,540,45,1,1,55,825,5160,15150,21642,15150,5160,825
%N A factorial-Pascal matrix.
%C Row sums are A162748.
%F Number triangle T(n,k)=sum{j=0..n, C(n,j)*C(n-j,2(k-j))*if(j<=k,(k-j)!,0)}.
%F G.f.: 1/(1-x-xy-x^2*y/(1-x-xy-x^2*y/(1-x-xy-2x^2*y/(1-x-xy-2x^2*y/(1-x-xy-3x^2*y/(1-... (continued fraction). [From _Paul Barry_, Apr 12 2010]
%e Triangle begins
%e 1,
%e 1, 1,
%e 1, 3, 1,
%e 1, 6, 6, 1,
%e 1, 10, 20, 10, 1,
%e 1, 15, 50, 50, 15, 1,
%e 1, 21, 105, 176, 105, 21, 1,
%e 1, 28, 196, 497, 497, 196, 28, 1,
%e 1, 36, 336, 1204, 1830, 1204, 336, 36, 1,
%e 1, 45, 540, 2604, 5634, 5634, 2604, 540, 45, 1,
%e 1, 55, 825, 5160, 15150, 21642, 15150, 5160, 825, 55, 1
%K easy,nonn,tabl
%O 0,5
%A _Paul Barry_, Jul 12 2009
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