A000175 Related to zeros of Bessel function.
1, 1, 2, 11, 38, 946, 4580, 202738, 3786092, 261868876, 1992367192, 2381255244240, 21411255538848, 2902625722978656, 451716954504285504, 319933105641374465472, 3761845343198709705600
Offset: 1
Keywords
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
- H. Jamke, Table of n, a(n) for n=1..100. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010]
- M. Delest, J.M. Fedou, Enumeration of skew Ferrers diagrams, preprint LaBRI nA degs 89, Bordeaux, Juin 1989 [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010]
- N. Kishore, The Rayleigh Polynomial, Proc. Amer. Math. Soc. 15, No. 6 (1964), pp. 911-917. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010]
- 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
Programs
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Mathematica
pi0[n_] := Product[k^Floor[n/k], {k, 1, n}]; J[v_, m_] := Sum[(-1)^n*(x/2)^( 2*n + v)/(n!*(n+v)!), {n, 0, m}] + O[x]^(2*m+v); p = J[1, 101]/(2*J[0, 101]); Reap[For[n=1, n <= 40, n += 2, Print["a(", (n+1)/2, ") = ", an = SeriesCoefficient[p, n]*pi0[(n+1)/2]*2^(n+1)]; Sow[an]]][[2, 1]] (* Jean-François Alcover, Feb 04 2016, adapted from Herman Jamke's 2nd PARI script *) -
PARI
alpha(k,n)=if(k
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PARI
pi0(n)=prod(k=1,n,k^floor(n/k)) J(v,m)=sum(n=0,m,(-1)^n*(x/2)^(2*n+v)/(n!*(n+v)!))+O(x^(2*m+v)) p=J(1,101)/(2*J(0,101));forstep(n=1,200,2,print((n+1)/2" "polcoeff(p,n)*pi0((n+1)/2)*2^(n+1))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010
Extensions
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010
Comments