|
|
A189731
|
|
a(n) = numerator of B(0,n) where B(n,n) = 0, B(n-1,n) = 1/n, and B(m,n) = B(m-1,n+1) - B(m-1,n).
|
|
3
|
|
|
0, 1, 1, 3, 2, 17, 4, 23, 25, 61, 18, 107, 40, 421, 1363, 1103, 210, 5777, 492, 7563, 24475, 19801, 2786, 103681, 33552, 135721, 146401, 355323, 39650, 1860497, 97108, 2435423, 2627065, 6376021, 20633238, 11128427, 1459960, 43701901
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Square array B(m,n) begins:
0, 1/1, 1/1, 3/2, 2/1, 17/6, ...
1/1, 0, 1/2, 1/2, 5/6, 7/6, ...
-1/1, 1/2, 0, 1/3, 1/3, 7/12, ...
3/2, -1/2, 1/3, 0, 1/4, 1/4, ...
-2/1, 5/6, -1/3, 1/4, 0, 1/5, ...
17/6, -7/6, 7/12, -1/4, 1/5, 0, ...
The inverse binomial transform of B(0,n) gives B(n,0) and thus it is an eigensequence in the sense that it remains the same (up to a sign) under inverse binomial transform.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
B:= proc(m, n) option remember;
if m=n then 0
elif n=m+1 then 1/n
elif n>m then B(m, n-1) +B(m+1, n-1)
else B(m-1, n+1) -B(m-1, n)
fi
end:
a:= n-> numer(B(0, n)):
|
|
MATHEMATICA
|
Rest[Numerator[Abs[CoefficientList[Normal[Series[Log[1 - x^2/(1 + x)], {x, 0, 40}]], x]]]] (* Vaclav Kotesovec, Jul 07 2020 *)
Table[Numerator[(LucasL[n]-1)/n], {n, 1, 38}] (* Artur Jasinski, Oct 21 2022 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|