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%I #9 Feb 22 2013 14:38:53
%S 1,1,1,1,2,2,2,1,1,3,5,8,10,10,10,8,5,3,1,1,4,9,18,31,46,64,82,96,106,
%T 110,106,96,82,64,46,31,18,9,4,1,1,5,14,33,68,124,210,332,492,693,931,
%U 1196,1476,1754,2008,2220,2374,2453,2453,2374,2220,2008,1754,1476,1196
%N Triangle T(n,k), 0<=k<=n, read by rows, defined by: Product{k=1..n, (1+x^k)^(n+1-k)} = Sum{k>=0, T(n,k)*x^k}.
%F T(n, k) = Sum {a_1, a_2, ...a_n with a_1+2*a_2+...+n*a_n=k, C(n, a_1)*C(n-1, a_2)*...*C(1, a_n)} .
%F Sum_{k, k>=0} T(n, k) = 2^(n*(n+1)/2), see A006125.
%e Row n=0 : 1
%e Row n=1 : 1, 1
%e Row n=2 : 1, 2, 2, 2, 1
%e Row n=3 : 1, 3, 5, 8, 10, 10, 10, 8, 5, 3, 1
%e Row n=4 : 1, 4, 9, 18, 31, 46, 64, 82, 96, 106, 110, 106, 96, 82, 64, 46, 31, 18, 9, 4, 1
%Y Cf. A006125.
%K easy,nonn,tabf
%O 0,5
%A _Philippe Deléham_, Jan 06 2004, Oct 16 2008
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