A247365 Central terms of triangles A102472 and A102473.

1, 2, 13, 130, 1807, 32280, 705421, 18237164, 544505521, 18438430990, 698246022001, 29239344782022, 1341545985079903, 66926098621724300, 3606825675219961657, 208826700420103831480, 12926842112341879416001, 851962999949978920707834, 59561112879709434549509941

Offset: 1

Author

Reinhard Zumkeller, Sep 14 2014

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A102472, A102473, A058294.

Programs

Haskell

a247365 n = a102473 (2 * n - 1) n

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 *)

Formula

a(n) = A102472(2*n-1,n) = A102473(2*n-1,n).

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