A000331 Related to zeros of Bessel function.

5, 14, 1026, 4324, 311387, 6425694, 579783114, 4028104212, 7315072725560, 61358264615344, 9569450876916944, 1632353370882506848, 1365475358484643531856, 15211641461623992544160, 74766806258361827981250240, 936580261005146914634459520, 6083678228249789825160175706880, 1936651082361926268672618636234240, 688115696843061332335070140230720000, 10517068622936239459488783307672335360, 2913914903970372007778735454555848514846720

Offset: 4

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is coefficient of nu in Rayleigh polynomial of index 2n.

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Matthew House, Table of n, a(n) for n = 4..195
• D. H. Lehmer, Zeros of the Bessel function J_{nu}(x), Math. Comp. 1 (1945), 405-407.
• D. H. Lehmer, Zeros of the Bessel function J_{nu}(x), Math. Comp., 1 (1943-1945), 405-407. [Annotated scanned copy]
• Index entries for sequences related to Bessel functions or polynomials

Crossrefs

Cf. A158616.

Programs

Mathematica

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;
Phi2n[n_, nu_] := 4^n*Product[(nu + k)^Floor[n/k], {k, 1, n}]*sig2n[n, nu];
a[n_] := Coefficient[Phi2n[n, x], x, 1];
Table[a[n], {n, 4, 24}] (* Jean-François Alcover, Dec 01 2023, after R. J. Mathar in A158616 *)

Extensions

More terms from Sean A. Irvine, Nov 11 2010