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

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

Offset

0,2

References

P. J. Davis, Interpolation and Approximation, Dover Publications, 1975, p. 93.

Links

Table of n, a(n) for n=0..43.

Example

a(0)=1, a(1)=2+2x, a(2)=6+12x-2x^2, ... approach 4^n*sqrt(x) near x=1.

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)

Crossrefs

Sequence in context: A350114 A275312 A209026 * A335311 A192933 A079005

Adjacent sequences: A091761 A091762 A091763 * A091765 A091766 A091767

Keyword

tabl,sign

Author

Michael Somos, Feb 04 2004

Status

approved