%I M3848 N1575 #31 Dec 01 2023 15:57:42
%S 5,14,1026,4324,311387,6425694,579783114,4028104212,7315072725560,
%T 61358264615344,9569450876916944,1632353370882506848,
%U 1365475358484643531856,15211641461623992544160,74766806258361827981250240,936580261005146914634459520,6083678228249789825160175706880,1936651082361926268672618636234240,688115696843061332335070140230720000,10517068622936239459488783307672335360,2913914903970372007778735454555848514846720
%N Related to zeros of Bessel function.
%C a(n) is coefficient of nu in Rayleigh polynomial of index 2n.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H D. H. Lehmer, <a href="http://dx.doi.org/10.1090/S0025-5718-45-99084-3">Zeros of the Bessel function J_{nu}(x)</a>, Math. Comp. 1 (1945), 405-407.
%H D. H. Lehmer, <a href="/A000175/a000175.pdf">Zeros of the Bessel function J_{nu}(x)</a>, Math. Comp., 1 (1943-1945), 405-407. [Annotated scanned copy]
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%t sig2n[n_, nu_] := sig2n[n, nu] = If[n == 1, 1/4/(nu + 1), Sum[sig2n[k, nu]*sig2n[n - k, nu], {k, 1, n - 1}]/(nu + n)] // Simplify;
%t Phi2n[n_, nu_] := 4^n*Product[(nu + k)^Floor[n/k], {k, 1, n}]*sig2n[n, nu];
%t a[n_] := Coefficient[Phi2n[n, x], x, 1];
%t Table[a[n], {n, 4, 24}] (* _Jean-François Alcover_, Dec 01 2023, after _R. J. Mathar_ in A158616 *)
%Y Cf. A158616.
%K nonn
%O 4,1
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Nov 11 2010