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 A285406 #50 Jun 27 2025 15:27:25
%S A285406 0,5,15,28,46,68,94,123,158,195,236,283,333,387,445,506,574,643,716,
%T A285406 794,875,961,1054,1146,1244,1346,1451,1562,1676,1794,1916,2041,2174,
%U A285406 2307,2444,2586,2731,2881,3034,3193,3356,3520,3690,3864,4041,4227,4413,4601,4796,4993
%N A285406 Base-2 logarithm of denominator of Sum_{k=0..n^2-1} (-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k)*n).
%C A285406 Needed for studying of Wallis-kind products of central binomials.
%F A285406 a(n) = A000523(A285389(n)).
%F A285406 a(n) = A056220(n) - A285717(n) = (2*(n^2)) - A007814(n) - A000120(n^2) - 1. - _Antti Karttunen_, Apr 28 2017, based on _Vladimir Shevelev_'s Jul 20 2009 formula in A000984
%t A285406 Log[2,Table[Denominator[Sum[Binomial[2k,k]/4^k,{k,0,n^2-1}]/n], {n,1,50}]]
%t A285406 Log[2,Denominator[Table[2^(1-2 n^2) n Binomial[2 n^2,n^2],{n,1,50}]]] (* _Ralf Steiner_, Apr 22 2017 *)
%o A285406 (PARI) a(n) = logint(denominator((2^(1 - 2*(n^2)))*n*binomial(2*(n^2), n^2)), 2); \\ _Indranil Ghosh_, Apr 27 2017
%o A285406 (PARI) val(n, p) = my(r=0); while(n, r+=n\=p);r
%o A285406 a(n) = 2*n^2-1 - valuation(n, 2) - val(2*n^2, 2) + 2*val(n^2, 2) \\ _David A. Corneth_, Apr 28 2017
%o A285406 (Python)
%o A285406 from sympy import binomial, integer_log, Integer
%o A285406 def a(n): return integer_log((Integer(2)**(1 - 2*n**2)*n*binomial(2*n**2, n**2)).denominator, 2)[0] # _Indranil Ghosh_, Apr 27 2017
%o A285406 (Scheme) (define (A285406 n) (- (* 2 n n) (A007814 n) (A000120 (* n n)) 1)) ;; _Antti Karttunen_, Apr 28 2017
%Y A285406 Cf. A000120, A000523, A000984, A007814, A011371, A056220, A201555, A285389, A281264, A285717.
%K A285406 nonn
%O A285406 1,2
%A A285406 _Ralf Steiner_, Apr 18 2017