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A322769
Main diagonal of array in A322765.
3
1, 4, 92, 5133, 537813, 91914202, 23456071495, 8411911367949, 4055497274641836, 2540939492105630071, 2014322292658946180922, 1977121111959534634757742, 2360026677940190304494287625, 3374607252811005168634470847052, 5706308288951111509370981721908854
OFFSET
0,2
REFERENCES
D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, page 778.
LINKS
FORMULA
a(n) = A346500(2n,n). - Alois P. Heinz, Jul 20 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(2*n, n):
seq(a(n), n=0..15); # 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[n, n];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Apr 29 2022 *)
CROSSREFS
Sequence in context: A003737 A362511 A265238 * A012071 A012217 A012135
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 30 2018
STATUS
approved