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A189731 a(n) = numerator of B(0,n) with 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.

The bisection of B(0,n) (odd part) gives A175385/A175386, and thus a(2*n+1) = A175385(n+1).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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 *)

CROSSREFS

Cf. A174341, A177690, A181722.

Sequence in context: A055864 A209600 A072045 * A126354 A158939 A173795

Adjacent sequences:  A189728 A189729 A189730 * A189732 A189733 A189734

KEYWORD

nonn

AUTHOR

Paul Curtz, Apr 26 2011

STATUS

approved

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Last modified April 10 18:49 EDT 2021. Contains 342853 sequences. (Running on oeis4.)