cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A063079 Bisection of A001790.

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%I A063079 #39 May 18 2020 04:03:09
%S A063079 1,5,63,429,12155,88179,1300075,9694845,583401555,4418157975,
%T A063079 67282234305,514589420475,15801325804719,121683714103007,
%U A063079 1879204156221315,14544636039226909,1804857108504066435
%N A063079 Bisection of A001790.
%H A063079 Vincenzo Librandi, <a href="/A063079/b063079.txt">Table of n, a(n) for n = 1..200</a>
%H A063079 Petros Hadjicostas, <a href="/A334907/a334907.pdf">Proof of the claim A334907(n)/n! = a(n+1)/A060818(n)</a>, 2020.
%F A063079 Numerators of binomial(2*n-3/2, -1/2).
%F A063079 Because A334907(n)/n! = a(n+1)/A060818(n) for n >= 0, the o.g.f. of a(n+1)/A060818(n), for n >= 0, is (sqrt(1 + sqrt(8*s)) - sqrt(1 - sqrt(8*s)))/sqrt(8*s * (1 - 8*s)), which is the e.g.f. of A334907 (see the link above for a proof). - _Petros Hadjicostas_, May 16 2020
%p A063079 seq(numer(binomial(2*n-3/2,-1/2)), n=1..20);
%t A063079 Numerator[Binomial[2Range[20]-3/2,-(1/2)]] (* _Harvey P. Dale_, Feb 27 2012 *)
%Y A063079 Cf. A001790, A060818, A334907. Other bisection gives A061548.
%K A063079 nonn,easy
%O A063079 1,2
%A A063079 _N. J. A. Sloane_, Aug 07 2001
%E A063079 More terms from _Vladeta Jovovic_, Aug 07 2001