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A189731 - OEIS
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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
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.
The bisection of B(0,n) (odd part) gives A175385/A175386, and thus a(2*n+1) = A175385(n+1).
LINKS
FORMULA
Numerator of (A000204(n) - 1)/n. - Artur Jasinski, Oct 21 2022
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)):
seq(a(n), n=0..50); # Alois P. Heinz, Apr 29 2011
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
Cf. A000204, A242926 (denominators).
Sequence in context: A055864 A209600 A072045 * A342140 A126354 A361084
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Apr 26 2011
STATUS
approved