A161200 - OEIS

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

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OFFSET

0,2

REFERENCES

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

LINKS

Table of n, a(n) for n=0..31.

FORMULA

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

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 *)

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.

Sequence in context: A337910 A092040 A293866 * A214747 A110766 A166314

Adjacent sequences: A161197 A161198 A161199 * A161201 A161202 A161203

KEYWORD

easy,sign,frac

AUTHOR

Johannes W. Meijer, Jun 08 2009

STATUS

approved