OFFSET
0,1
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..300
FORMULA
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..22); # Alois P. Heinz, Jul 21 2021
MATHEMATICA
P[m_, n_] := P[m, n] = If[n == 0, BellB[m], (1/2)(P[m+2, n-1] + P[m+1, n-1] + Sum[Binomial[n-1, k] P[m, k], {k, 0, n-1}])];
a[n_] := P[2, n];
Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Apr 29 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 30 2018
STATUS
approved