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%I #8 Apr 17 2013 12:28:26
%S 1,1,1,0,1,1,0,2,1,0,0,2,1,0,1,2,1,0,0,1,2,1,0,1,1,2,1,0,0,1,1,2,1,0,
%T 1,1,1,2,1,0,0,1,1,1,2,1,0,1,1,1,1,2,1,0,0,1,1,1,1,2,1,0,1,1,1,1,1,2,
%U 1,0,0,1,1,1,1,1,2,1,0,1,1,1,1,1,1,2,1
%N Irregular triangle T(n,k), read by rows; row n gives coefficients in expansion of P_n(x), which is defined by: P_0(x) = 1, P_n(x) = P_(n-1)(x)+x if n odd, P_n(x) = P_(n-1)(x)*x if n even.
%C Row lengths are: 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, ...
%F Sum_(T(n,k)*x^k, k>=0) = A019590(n+1), A008619(n+1), A123208(n) for x = 0, 1, 2 respectively.
%e Irregular triangle begins:
%e 1
%e 1, 1
%e 0, 1, 1
%e 0, 2, 1
%e 0, 0, 2, 1
%e 0, 1, 2, 1
%e 0, 0, 1, 2, 1
%e 0, 1, 1, 2, 1
%e 0, 0, 1, 1, 2, 1
%e 0, 1, 1, 1, 2, 1
%e 0, 0, 1, 1, 1, 2, 1
%e 0, 1, 1, 1, 1, 2, 1
%e 0, 0, 1, 1, 1, 1, 2, 1
%e 0, 1, 1, 1, 1, 1, 2, 1
%e ...
%Y Cf. A219605.
%K nonn,tabf
%O 0,8
%A _Philippe Deléham_, Apr 13 2013
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