A000331 Related to zeros of Bessel function. (Formerly M3848 N1575)

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

Offset

4,1

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

Table of n, a(n) for n=4..24.

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

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 *)

Crossrefs

Cf. A158616.

Sequence in context: A027832 A128946 A156219 * A353610 A306155 A082269

Adjacent sequences: A000328 A000329 A000330 * A000332 A000333 A000334

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 11 2010

Status

approved