OFFSET
1,3
COMMENTS
Constant term of the Rayleigh polynomials. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010]
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]
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 *)
PROG
(PARI) alpha(k, n)=if(k<floor(n/2), 2, if(n%2==1, 2, 1))
e(r, k, n)=floor(n/r)-floor(k/r)-floor((n-k)/r)
phi2(n)=if(n<3, return(1), return(sum(k=1, floor(n/2), alpha(k, n)*phi2(k)*phi2(n-k)*prod(r=1, n-1, (v+r)^e(r, k, n)))))
for(m=1, 30, print1(polcoeff(phi2(m), 0)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010
STATUS
approved