OFFSET
1,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..300
FORMULA
a(n) = y(n,n), where y(m+2,n) = (m + n)*y(m+1,n) + y(m,n), with y(0,n)=0, y(1,n)=1 for all n. - Benedict W. J. Irwin, Nov 03 2016
a(n) = round(2*BesselI(n-1,2)*BesselK(2*n-1,2)). - Mark van Hoeij, Nov 08 2022
a(n) ~ 2^(2*n - 3/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Nov 09 2022
a(n) = (-1)^n * (A001040(n-1) * A001053(2*n-1) - A001053(n-1) * A001040(2*n-1)). - Mark van Hoeij, Jul 10 2024
MAPLE
seq(round(2*BesselI(n-1, 2)*BesselK(2*n-1, 2)), n=1..30); # Mark van Hoeij, Nov 08 2022
A001040 := proc(n) options remember;
if n < 2 then n else (n - 1)*procname(n-1) + procname(n-2) fi
end:
A001053 := proc(n) options remember;
if n < 2 then 1-n else (n - 1)*procname(n-1) + procname(n-2) fi
end:
seq( (-1)^n * (A001040(n-1) * A001053(2*n-1) - A001053(n-1) * A001040(2*n-1)), n=1..30); # Mark van Hoeij, Jul 10 2024
MATHEMATICA
Table[DifferenceRoot[Function[{y, m}, {y[2+m]==(m+n)y[1+m]+y[m], y[0]==0, y[1]==1}]][n], {n, 1, 20}] (* Benedict W. J. Irwin, Nov 03 2016 *)
PROG
(Haskell)
a247365 n = a102473 (2 * n - 1) n
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 14 2014
STATUS
approved