A000167 Nearest integer to modified Bessel function K_n(2).

0, 0, 0, 1, 2, 9, 49, 306, 2188, 17810, 162482, 1642635, 18231462, 220420179, 2883693795, 40592133316, 611765693528, 9828843229764, 167702100599524, 3028466654021205, 57708568527002410, 1157199837194069405

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

• Alois P. Heinz, 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: A000167 := proc(n) round( evalf ( BesselK( n,2 ) )); end;

Mathematica

Table[BesselK[n, 2] // Round, {n, 0, 21}] (* Jean-François Alcover, Mar 12 2014 *)

PARI

a(n)=round(besselk(n,2)) \\ Charles R Greathouse IV, Jul 29 2016

Formula

b(n) = (n-1)*b(n-1) + b(n-2) with b(n) = K_n(2). - Christian Krause, Dec 08 2023

Extensions

More terms from Herman P. Robinson