A019267 From an asymptotic expansion for Pi.

1, 1, 1, -1, -5, 23, 53, -593, -5165, 110123, 231743, -8113223, -33497425, 1744764499, 3563384029, -258115578289, -4191097954685, 402402297433523, 813628574192123, -99925014024526283, -403078530716889835, 61606956815080291849

Offset: 0

Author

Simon Plouffe

Keywords

• sign

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 481.

Crossrefs

Cf. A002894.

Programs

Maple

v := asympt(16^n/(2*n)!^2*n!^4/n,n,24); seq(numer(op(i,v)),i=1..nops(v));

Mathematica

nmax = 20; Numerator[CoefficientList[Series[Binomial[2 n, n]^2/(2^(4 n)/Pi/n), {n, Infinity, nmax}], 1/n]]*(-1)^Range[0, nmax] (* Vaclav Kotesovec, Sep 27 2019 *)