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

1,2

Links

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

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

Maple

seq(round(2*BesselI(n-1, 2)*BesselK(2*n-1, 2)), n=1..30); # Mark van Hoeij, Nov 08 2022

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

Cf. A102472, A102473, A058294.

Sequence in context: A259611 A351299 A215624 * A107721 A085882 A041509

Adjacent sequences: A247362 A247363 A247364 * A247366 A247367 A247368

Keyword

nonn

Author

Reinhard Zumkeller, Sep 14 2014

Status

approved