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 A378130 #11 Mar 31 2025 01:46:43
%S A378130 9,9,9,9,9,6,3,8,3,1,5,9,0,8,4,1,2,7,7,7,2,7,6,3,4,9,9,1,8,4,7,0,6,1,
%T A378130 1,2,8,0,8,9,4,3,4,8,8,7,7,0,3,5,9,6,6,1,3,2,9,0,9,5,9,5,0,4,9,2,6,8,
%U A378130 1,5,2,7,3,9,9,2,1,6,4,9,2,2,9,9,3,7,4,7,9,1
%N A378130 Decimal expansion of 24*L^2/(5^(7/4)*Pi^2), where L is the lemniscate constant (A062539).
%H A378130 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lemniscate_constant">Lemniscate constant</a> (includes this constant).
%H A378130 <a href="/index/Ga#gamma_function">Index to sequences related to the Gamma function</a>.
%F A378130 Equals 12*Pi/(5^(7/4)*Gamma(3/4)^4) = 12*A091670/5^(7/4).
%F A378130 Equals Sum_{k >= 0} ((-1)^k/6635520^k)*(4*k)!/(k!)^4 = Sum_{k >= 0} ((-1)^k/6635520^k)*A008977(k).
%F A378130 Equals pFq(1/4, 1/2, 3/4; 1, 1; -1/25920), where pFq is the generalized hypergeometric function.
%e A378130 0.999996383159084127772763499184706112808943488770...
%t A378130 First[RealDigits[12*Pi/(5^(7/4)*Gamma[3/4]^4), 10, 100]] (* or *)
%t A378130 First[RealDigits[Sum[((-1)^k/6635520^k)*(4*k)!/k!^4, {k, 0, Infinity}], 10, 100]] (* or *)
%t A378130 First[RealDigits[HypergeometricPFQ[{1/4, 1/2, 3/4}, {1, 1}, -1/25920], 10, 100]]
%Y A378130 Cf. A008977, A062539, A091670.
%Y A378130 Cf. A377999, A378128, A378129, A378129, A378131, A378132.
%K A378130 nonn,cons,easy
%O A378130 0,1
%A A378130 _Paolo Xausa_, Nov 18 2024