0,2

Also denominator of e(0,n) (see Maple line). - N. J. A. Sloane (njas(AT)research.att.com), Feb 16 2002.

Denominator of coefficient of x^n in (1+x)^(k/2) or (1-x)^(k/2) for any odd integer k. - Michael Somos, Sep 15 2004

a(n)=4^n/2^A000120(n). - Michael Somos, Sep 15 2004

Numerator of binomial(2n,n)/4^n = A001790(n).

Denominators in expansion of sqrt(c(x)), c(x) the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Jul 12 2005

Denominator of 2^m*GAMMA(m+3/4)/(GAMMA(3/4)*GAMMA(m+1)). - Stephen Crowley (crow(AT)crowlogic.net), Mar 19 2007

Denominator in expansion of Jacobi_P(n,1/2,1/2,x). - Paul Barry (pbarry(AT)wit.ie), Feb 13 2008

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009: (Start)

This sequence equals the denominators of the coefficients of the series expansions of (1-x)^((-1-2*n)/2) for all integer values of n; see A161198 for detailed information.

. (End)

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 513, Eq. (7.282).

V. H. Moll. The evaluation of integrals: a personal story, Notices Amer. Math. Soc., 49 (No. 3, March 2002), 311-317.

T. D. Noe, Table of n, a(n) for n=0..200

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Legendre Polynomial

Eric Weisstein's World of Mathematics, Binomial Series

Eric Weisstein's World of Mathematics, Random Matrix

a(n)=2^(2n-1-A048881(n-1)), if n>0.

sqrt(1+x) = 1+1/2*x-1/8*x^2+1/16*x^3-5/128*x^4+7/256*x^5-21/1024*x^6+33/2048*x^7+...

binomial(2n,n)/4^n => 1, 1/2, 3/8, 5/16, 35/128, 63/256, 231/1024, 429/2048, 6435/32768, ...

The sequence e(0,n) begins 1, 3/2, 21/8, 77/16, 1155/128, 4389/256, 33649/1024, 129789/2048, 4023459/32768 ...

e := proc(l, m) local k; add(2^(k-2*m)*binomial(2*m-2*k, m-k)*binomial(m+k, m)*binomial(k, l), k=l..m); end;

Z[0]:=0: for k to 30 do Z[k]:=simplify(1/(2-z*Z[k-1])) od: g:=sum((Z[j]-Z[j-1]), j=1..30): gser:=series(g, z=0, 27): seq(denom(coeff(gser, z, n)), n=-1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 21 2008

a[n_, m_] := Binomial[n - m/2 + 1, n - m + 1] - Binomial[n - m/2, n - m + 1]; s[n_] := Sum[ a[n, k], {k, 0, n}]; Table [Denominator[s[n]], {n, 0, 26}] - Michele Dondi (bik.mido@tiscalinet.it), Jul 11, 2002

(PARI) a(n)=if(n<0, 0, denominator(binomial(2*n, n)/4^n)) /* Michael Somos, Sep 15 2004 */

Cf. A001790, A001803, A002596, A005187, A072287, A067002.

a(n) = 2^A005187(n).

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 2009: (Start)

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

(End)

Adjacent sequences: A046158 A046159 A046160 this_sequence A046162 A046163 A046164

Sequence in context: A098232 A100736 A099888 this_sequence A092978 A101059 A101658

nonn,easy,nice,frac,new

Eric Weisstein (eric(AT)weisstein.com)