A322772 Row 2 of array in A322770.

2, 9, 70, 801, 12347, 243235, 5908978, 172449180, 5925731200, 235946129714, 10745098631229, 553630279110396, 31978001903989065, 2054387367168242251, 145795148420558536232, 11361381129471379493270, 967044630942570464100761, 89483154423059719127570924, 8963545185499520505954151682

Offset

0,1

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Formula

a(n) = A346517(n,n+2) = A346517(n+2,n). - Alois P. Heinz, Jul 21 2021

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-j)*binomial(n-1, j-1), j=1..n))
    end:
A:= proc(n, k) option remember; `if`(n<k, A(k, n),
     `if`(k=0, b(n), (A(n+1, k-1)-add(A(n-k+j, j)
      *binomial(k-1, j), j=0..k-1)+A(n, k-1))/2))
    end:
a:= n-> A(n, n+2):
seq(a(n), n=0..18);  # Alois P. Heinz, Jul 21 2021

Mathematica

Q[m_, n_] := Q[m, n] = If[n == 0, BellB[m], (1/2)(Q[m+2, n-1] + Q[m+1, n-1] - Sum[Binomial[n-1, k] Q[m, k], {k, 0, n-1}])];
a[n_] := Q[2, n];
Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Apr 29 2022 *)

Crossrefs

Cf. A322770, A346517.

Sequence in context: A014500 A101482 A099717 * A177450 A193469 A336606

Adjacent sequences: A322769 A322770 A322771 * A322773 A322774 A322775

Keyword

nonn

Author

N. J. A. Sloane, Dec 30 2018

Status

approved