|
| |
|
|
A322766
|
|
Row 1 of array in A322765.
|
|
3
|
|
|
|
1, 4, 26, 249, 3274, 56135, 1207433, 31638625, 987249425, 36030130677, 1515621707692, 72603595393584, 3920675798922189, 236615520916677436, 15840357595697061964, 1168697367186883073296, 94486667847573203169757, 8328527812527985862657297, 796762955545266206229493979
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
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
|
a(n) = A346500(n,n+1) = A346500(n+1,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+1):
seq(a(n), n=0..22); # Alois P. Heinz, Jul 21 2021
|
|
|
MATHEMATICA
|
b[n_] := b[n] = If[n == 0, 1,
Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]];
A[n_, k_] := A[n, k] = If[n < k, A[k, n],
If[k == 0, b[n], (A[n+1, k - 1] + Sum[A[n - k + j, j]*
Binomial[k-1, j], {j, 0, k - 1}] + A[n, k - 1])/2]];
a[n_] := A[n, n + 1]; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jun 01 2022, after Alois P. Heinz *)
|
|
|
CROSSREFS
|
Cf. A322765, A346500.
Sequence in context: A210918 A052880 A090357 * A160886 A192546 A213438
Adjacent sequences: A322763 A322764 A322765 * A322767 A322768 A322769
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane, Dec 30 2018
|
|
|
STATUS
|
approved
|
| |
|
|
