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.
%I A004130 #31 May 09 2014 02:05:10
%S A004130 1,1,5,15,195,663,4641,16575,480675,1762475,13042315,48612265,
%T A004130 729183975,2748462675,20809788825,79077197535,4823709049635,
%U A004130 18443593425075,141400882925575,543277076503525,8366466978154285,32270658344309385
%N A004130 Numerators in expansion of (1-x)^{-1/4}.
%C A004130 Numerators in expansion of sqrt(1/sqrt(1-4x)). - _Paul Barry_, Jul 12 2005
%C A004130 Denominators are in A088802. - _Michael Somos_, Aug 23 2007
%H A004130 Vincenzo Librandi, <a href="/A004130/b004130.txt">Table of n, a(n) for n = 0..1000</a>
%F A004130 a(n) = prod(k=1, n, (4k-3)/k * 2^A007814(k)), proved by _Mitch Harris_, following a conjecture by _Ralf Stephan_.
%F A004130 a(n) = 2^(e_2((2n)!)-n)/n! Product[4k+1,{k,0,n-1}], where e_2((2n)!) is the highest power of 2 that divides (2n)! (sequence A005187). - _Emanuele Munarini_, Jan 25 2011
%F A004130 Numerators in (1-4t)^(-1/4) = 1 + t + (5/2)t^2 + (15/2)t^3 + (195/8)t^4 + (663/8)t^5 + (4641/16)t^6 + (16575/16)t^7 + ... = 1 + t + 5*t^2/2! + 45*t^3/3! + 585*t^4/4! + ... = e.g.f. for the quartic factorials A007696 (cf. A094638). - _Tom Copeland_, Dec 04 2013
%t A004130 Table[Numerator[Binomial[-1/4, n] (-1)^n], {n, 0, 20}]
%o A004130 (PARI) {a(n) = if( n<0, 0, numerator( polcoeff( (1 - x +x*O(x^n))^(-1/4), n ) ) ) } /* _Michael Somos_, Aug 23 2007 */
%Y A004130 Cf. A004134, A004981, A034255, A034385, A048882, A007696, A000265, A049606.
%K A004130 nonn,frac
%O A004130 0,3
%A A004130 _N. J. A. Sloane_