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 A088801 #12 Feb 16 2025 08:32:51
%S A088801 1,-3,-7,-9,59,483,-2323,-42801,923923,30055311,-170042041,
%T A088801 -8639161167,99976667055,7336972779615,-42962450319915,
%U A088801 -4309733345367105,203289825295660035,26751125064470578695,-158415664732997134045,-26488943422458070446915
%N A088801 Numerators of coefficients of powers of n^(-1) in the Romanovsky series expansion of the mean of the standard deviation from a normal population.
%C A088801 Asymptotic expansion of Gamma(N/2) / Gamma((N-1)/2) = (N/2)^(1/2) * (c(0) + c(1)/N + c(2)/N^2 + ... ). a(n) = numerator(c(n)). - _Michael Somos_, Aug 23 2007
%H A088801 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StandardDeviationDistribution.html">Standard Deviation Distribution</a>
%e A088801 b(N) = 1 - 3/(4N) - 7/(32N^2) - 9/(128N^3) + ...
%t A088801 a[ n_] := If[ n < 0, 0, Module[{A = 1}, Do[ A += x^k / (4 k) SeriesCoefficient[ (A /. x -> x / (1 + 2 x))^2 - (A/(1 - x))^2 / (1 + 2 x) + O[x]^(k + 2), k + 1], {k, n}]; Numerator@Coefficient[A, x, n]]]; (* _Michael Somos_, May 24 2015 *)
%o A088801 (PARI) {a(n) = my(A); if(n < 0, 0, A = 1 + O(x) ; for( k = 1, n, A = truncate(A) + x^2 * O(x^k); A += x^k/4/k * polcoeff( subst( A, x, x/(1+2*x))^2 - A^2/(1-x)^2/(1+2*x), k+1 ) ); numerator( polcoeff( A, n ) ) ) }; /* _Michael Somos_, Aug 23 2007 */
%Y A088801 Cf. A088802.
%K A088801 sign,frac
%O A088801 0,2
%A A088801 _Eric W. Weisstein_, Oct 16 2003
%E A088801 a