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A091764 Triangle of coefficients of n-th degree interpolating polynomial to sqrt(x) multiplied by 4^n. 0

%I

%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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Last modified August 12 05:33 EDT 2020. Contains 336438 sequences. (Running on oeis4.)