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 A376228 #18 Oct 24 2024 05:00:38 %S A376228 1,56,2808,152000,8575000,496093248,29188893888,1738242215424, %T A376228 104455598247000,6321316756040000,384702925005146176, %U A376228 23520160000755565056,1443504313932496274368,88879637239345064000000,5487711609457595160000000,339644002672064899081728000,21065385579274083203741943000 %N A376228 a(n) = (6*n+1) * (2*n)!^3 / n!^6. %H A376228 S. Ramanujan, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram06.pdf">Modular equations and approximations to Pi</a>, Quarterly Journal of Mathematics, XLV, 1914, p. 45. %F A376228 a(n) = (6*n+1) * A002897(n). %F A376228 a(n) ~ 3*2^(6*n+1)/sqrt(n*Pi^3). - _Stefano Spezia_, Oct 17 2024 %F A376228 D-finite with recurrence n^3*a(n) +8*(56*n^3-252*n^2+330*n-141)*a(n-1) -4096*(2*n-3)^3*a(n-2)=0. - _R. J. Mathar_, Oct 24 2024 %e A376228 G.f.: A(x) = 1 + 56*x + 2808*x^2 + 152000*x^3 + 8575000*x^4 + 496093248*x^5 + 29188893888*x^6 + 1738242215424*x^7 + ... %e A376228 where %e A376228 A(x) = 1 + 7*(1/2)^3*64*x + 13*((1*3)/(2*4))^3*64^2*x^2 + 19*((1*3*5)/(2*4*6))^3*64^3*x^3 + 25*((1*3*5*7)/(2*4*6*8))^3*64^4*x^4 + ... + (6*n+1)*(2*n)!^3/n!^6*x^n + ... %e A376228 SPECIFIC VALUES. %e A376228 At x = 1/256 we have the series %e A376228 4/Pi = 1 + 7*(1/2)^3/4 + 13*((1*3)/(2*4))^3/4^2 + 19*((1*3*5)/(2*4*6))^3/4^3 + 25*((1*3*5*7)/(2*4*6*8))^3/4^4 + ... = 1.273239544735162686... %e A376228 see formula 28 in the Ramanujan link for details. %t A376228 a[n_]:=(6*n+1) * (2*n)!^3 / n!^6; Array[a,17,0] (* _Stefano Spezia_, Oct 17 2024 *) %Y A376228 Cf. A002897. %K A376228 nonn %O A376228 0,2 %A A376228 _Paul D. Hanna_, Oct 17 2024