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 A384542 #14 Jun 03 2025 01:11:31 %S A384542 1,1666,1090054,485318932,176760328262,56963958713340, %T A384542 16909346921973660,4732136004374122344,1266899066122354262598, %U A384542 327667319343098397330668,82435716917761454374571444,20275150472587631020453400984,4893425028040341625551135687452,1162305136998381407493307772297560 %N A384542 Expansion of g.f. sinh(7*arctanh(14*sqrt(x)))/(98*sqrt(x)). %F A384542 a(n) = 49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2). %F A384542 O.g.f.: (1 + 980*x + 115248*x^2 + 1075648*x^3)/(-196*x + 1)^(7/2). %F A384542 E.g.f.: exp(98*x)*(BesselI(0, 98*x)*(275365888*x^3 + 5444096*x^2 + 23520*x + 15) + 224*x*BesselI(1, 98*x)*(1229312*x^2 + 18032*x + 29))/15. %t A384542 a[n_]:=49^n*(105 + 464*n + 704*n^2 + 512*n^3)*(2*n)!/(105*(n!)^2); Array[a,14,0] (* _Stefano Spezia_, Jun 02 2025 *) %Y A384542 Cf. A383928, A384335, A285043, A285044, A285045, A285046, A384417. %K A384542 nonn %O A384542 0,2 %A A384542 _Karol A. Penson_, Jun 02 2025