A161200 Numerators in expansion of (1-x)^(3/2).

1, -3, 3, 1, 3, 3, 7, 9, 99, 143, 429, 663, 4199, 6783, 22287, 37145, 1002915, 1710855, 5892945, 10235115, 71645805, 126233085, 447553665, 797813055, 11435320455, 20583576819, 74417546961, 135054066707, 983965343151, 1798281489207, 6593698793759, 12123897782073

Offset: 0

Author

Johannes W. Meijer, Jun 08 2009

Keywords

• easy
• sign
• frac

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 6, equation 6:14:5 at page 50.

Crossrefs

Cf. A002596 ((1-x)^(1/2)) and A161202 ((1-x)^(5/2)).

Cf. A161199 (numerators in expansion of (1-x)^(-5/2)).

Cf. A161198 (triangle related to the series expansions of (1-x)^((-1-2*n)/2) for all values of n).

Cf. A046161 (denominators of the series expansions of (1-x)^(3/2)).

Cf. A000302, A000984.

Programs

Mathematica

Numerator[CoefficientList[Series[(1-x)^(3/2),{x,0,30}],x]] (* Harvey P. Dale, Aug 26 2016 *)
a[n_]:= Numerator[3/(3-8*n+4*n^2)*Binomial[2*n,n]/(4^n)]; Array[a,28,0] (* Stefano Spezia, Dec 29 2024 *)

Formula

a(n) = numerator((3/(3-8*n+4*n^2))*binomial(2*n,n)/4^n).