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A091764
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Triangle of coefficients of n-th degree interpolating polynomial to sqrt(x) multiplied by 4^n.
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0
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1, 2, 2, 6, 12, -2, 20, 60, -20, 4, 70, 280, -140, 56, -10, 252, 1260, -840, 504, -180, 28, 924, 5544, -4620, 3696, -1980, 616, -84, 3432, 24024, -24024, 24024, -17160, 8008, -2184, 264, 12870, 102960, -120120, 144144, -128700, 80080, -32760, 7920
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| P. J. Davis, Interpolation and Approximation, Dover Publications, 1975, p. 93.
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EXAMPLE
| a(0)=1, a(1)=2+2x, a(2)=6+12x-2x^2, ... approach 4^n*sqrt(x) near x=1.
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PROG
| (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)
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CROSSREFS
| Sequence in context: A153897 A103774 A036052 * A192933 A079005 A178802
Adjacent sequences: A091761 A091762 A091763 * A091765 A091766 A091767
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KEYWORD
| tabl,sign
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AUTHOR
| Michael Somos, Feb 04 2004
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