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%I #2 Apr 30 2014 01:33:21
%S 1,2,2,6,12,-2,20,60,-20,4,70,280,-140,56,-10,252,1260,-840,504,-180,
%T 28,924,5544,-4620,3696,-1980,616,-84,3432,24024,-24024,24024,-17160,
%U 8008,-2184,264,12870,102960,-120120,144144,-128700,80080,-32760,7920
%N Triangle of coefficients of n-th degree interpolating polynomial to sqrt(x) multiplied by 4^n.
%D P. J. Davis, Interpolation and Approximation, Dover Publications, 1975, p. 93.
%e a(0)=1, a(1)=2+2x, a(2)=6+12x-2x^2, ... approach 4^n*sqrt(x) near x=1.
%o (PARI) T(n,k)=polcoeff((4^n)*sum(k=1,n,-(1-x)^k*(2*k-2)!/(k-1)!/k!/2^(2*k-1),1),k)
%K tabl,sign
%O 0,2
%A _Michael Somos_, Feb 04 2004
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