A000155 Nearest integer to modified Bessel function K_n(1).

0, 1, 2, 7, 44, 361, 3654, 44207, 622552, 10005041, 180713290, 3624270839, 79914671748, 1921576392793, 50040900884366, 1403066801155039, 42142044935535536, 1349948504738292193, 45940391206037470098

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 429.
• 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

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• Index entries for sequences related to Bessel functions or polynomials

Programs

Maple

Digits := 60: A000155 := proc(n) round( evalf ( BesselK( n, 1) )); end;
a := proc(n) options remember;if n<3 then n elif n=3 then 7 else a(n-4)+2*(n-3)*a(n-3)+2*(n-1)*a(n-1) fi end: # Mark van Hoeij, Nov 21 2011
series(hypergeom([1,1],[],2*x/(1+x^2))*x/(1+x^2), x=0, 20); # Mark van Hoeij, Nov 21 2011

Mathematica

Table[Round[BesselK[n, 1]], {n, 0, 18}] (* Ray Chandler, Nov 28 2006 *)

PARI

a(n)=round(besselk(n,1)) \\ Charles R Greathouse IV, May 11 2016

Extensions

Extended by Ray Chandler, Nov 28 2006

More accurate definition by Sean A. Irvine, Mar 28 2010