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A067002 Numerator of sum_{k=0..n} 2^(k-2n) *binomial(2n-2k,n-k)* binomial(n+k,n). 2
1, 3, 21, 77, 1155, 4389, 33649, 129789, 4023459, 15646785, 122044923, 477084699, 7474326951, 29322359577, 230389968105, 906200541213, 57090634096419, 225004263791769, 1775033636579511, 7006711723340175, 110706045228774765 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numerator of e(0,n) (see Maple line).

The generating function of the full fraction is (1-2*x)^(-3/4). - R. J. Mathar, Nov 06 2011

LINKS

Table of n, a(n) for n=0..20.

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

FORMULA

Numerator of 2^n*Gamma(n+3/4)/(Gamma(3/4)*n!). - R. J. Mathar, Nov 06 2011

Numerator of integral_{x>0} 1/(x^4+1)^(n+1) / (Pi*sqrt(2)). [Jean-Fran├žois Alcover, Apr 29 2013]

EXAMPLE

1, 3/2, 21/8, 77/16, 1155/128, 4389/256, 33649/1024, 129789/2048, 4023459/32768 ... = A067002/A046161

MAPLE

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;

MATHEMATICA

Numerator[Table[Sum[2^(k-2n) Binomial[2n-2k, n-k]Binomial[n+k, n], {k, 0, n}], {n, 0, 30}]] (* Harvey P. Dale, Oct 19 2012 *)

CROSSREFS

Denominators are in A046161.

Sequence in context: A054646 A228317 A109721 * A110450 A102832 A112851

Adjacent sequences:  A066999 A067000 A067001 * A067003 A067004 A067005

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Feb 16 2002

STATUS

approved

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Last modified October 20 19:44 EDT 2018. Contains 316401 sequences. (Running on oeis4.)