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A158616 Table of expansion coefficients [x^m] of the Rayleigh polynomial of index 2n. 2
1, 1, 2, 11, 5, 38, 14, 946, 1026, 362, 42, 4580, 4324, 1316, 132, 202738, 311387, 185430, 53752, 7640, 429, 3786092, 6425694, 4434158, 1596148, 317136, 33134, 1430, 261868876, 579783114, 547167306, 287834558, 92481350, 18631334, 2305702 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..35.

Nand Kishore, The Rayleigh Polynomial, Proc. AMS 15 (6) (1964) 911-917.

Nand Kishore, The Rayleigh Function, Proc. AMS 14 (4) (1963) 527-533.

D. H. Lehmer, Zeros of the Bessel function J_{nu}(x), Math. Comp. 1 (1945), 405-407. Gives first 12 rows.

D. H. Lehmer, Zeros of the Bessel function J_{nu}(x), Math. Comp., 1 (1943-1945), 405-407. Gives first 12 rows. [Annotated scanned copy]

EXAMPLE

The polynomials of low index are Phi(2,x)=Phi(4,x) = 1 ; Phi(6,x)=2 ; Phi(8,x)=11+5x ; Phi(10,x)=38+14x ; Phi(12,x)=946+1026x+362x^2+42x^3 ;

Triangle begins:

1,

1,

2,

11,5,

38,14,

946,1026,362,42,

4580,4324,1316,132,

202738,311387,185430,53752,7640,429,

...

MAPLE

sig2n := proc(n, nu) option remember ; if n = 1 then 1/4/(nu+1) ; else add( procname(k, nu)*procname(n-k, nu), k=1..n-1)/(nu+n) ; simplify(%) ; fi; end:

Phi2n := proc(n, nu) local k ; 4^n*mul( (nu+k)^(floor(n/k)), k=1..n)*sig2n(n, nu) ; factor(%) ; end:

for n from 1 to 14 do rpoly := Phi2n(n, nu) ; print(coeffs(rpoly)) ; od:

CROSSREFS

Cf. A000992, A000175 (first column), A000331 (2nd column).

Sequence in context: A009301 A087552 A124688 * A127821 A114724 A226219

Adjacent sequences:  A158613 A158614 A158615 * A158617 A158618 A158619

KEYWORD

nonn,tabf

AUTHOR

R. J. Mathar, Mar 22 2009

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)