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URL: https://oeis.org/A000155

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A000155
Nearest integer to modified Bessel function K_n(1).
2
0, 1, 2, 7, 44, 361, 3654, 44207, 622552, 10005041, 180713290, 3624270839, 79914671748, 1921576392793, 50040900884366, 1403066801155039, 42142044935535536, 1349948504738292193, 45940391206037470098, 1655204031922087215719, 62943693604245351667420, 2519402948201736153912521
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
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].
FORMULA
Conjecture: a(n) = Integral_{x=0..oo} ChebyshevU(n - 1, x)/exp(x) dx, where ChebyshevU(n, x) is the n-th Chebyshev polynomial of the second kind with variable x. - Velin Yanev, Jan 14 2026
a(n) ~ (n-1)! * 2^(n-1). - Vaclav Kotesovec, Feb 09 2026
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
KEYWORD
nonn
EXTENSIONS
Extended by Ray Chandler, Nov 28 2006
More accurate definition by Sean A. Irvine, Mar 28 2010
STATUS
approved