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A000331
Related to zeros of Bessel function.
(Formerly M3848 N1575)
2
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
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]
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
KEYWORD
nonn,changed
EXTENSIONS
More terms from Sean A. Irvine, Nov 11 2010
STATUS
approved