A000155 Nearest integer to modified Bessel function K_n(1). (Formerly M1810 N0716)

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

Offset

0,3

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

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 *)

Prog

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

Crossrefs

Sequence in context: A158107 A145073 A111561 * A077045 A178012 A194018

Adjacent sequences: A000152 A000153 A000154 * A000156 A000157 A000158

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Extended by Ray Chandler, Nov 28 2006

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

Status

approved