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A178904 This should be related to the Coxeter transformations of the posets of partitions in rectangular boxes of size m times n. 5
1, -1, -1, 0, -1, 0, 0, 1, 1, 0, 0, -1, 1, -1, 0, 0, 1, -1, -1, 1, 0, 0, -1, 2, -3, 2, -1, 0, 0, 1, -3, 4, 4, -3, 1, 0, 0, -1, 3, -6, 8, -6, 3, -1, 0, 0, 1, -3, 9, -13, -13, 9, -3, 1, 0, 0, -1, 4, -11, 19, -23, 19, -11, 4, -1, 0, 0, 1, -5, 13, -27, 39, 39, -27, 13, -5, 1, 0, 0, -1, 5, -17, 38, -61, 71, -61, 38, -17, 5, -1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,24

COMMENTS

This table is symmetric: a(m,n)=a(n,m) for all m,n>=0.

LINKS

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

EXAMPLE

a(0,0) = 1, a(1,0) = a(0,1) = -1.

Triangle begins:

   1;

  -1, -1;

   0, -1,  0;

   0,  1,  1,  0;

   0, -1,  1, -1,  0;

   0,  1, -1, -1,  1,  0;

   0, -1,  2, -3,  2, -1, 0;

   ...

MATHEMATICA

b[m_, n_] := (-1)^Max[m, n]*Binomial[m+n, n]; A[m_, n_] := DivisorSum[ n+m+1, b[Floor[m/#], Floor[n/#]]*MoebiusMu[#]&]/(m+n+1); Table[A[m-n, n], {m, 0, 12}, {n, 0, m}] // Flatten (* Jean-Fran├žois Alcover, Feb 23 2017, adapted from Python *)

PROG

(Python)

def twisted_binomial(m, n):

    return (-1)**max(m, n)*binomial(m+n, n)

def coefficients_A(m, n):

    return add(twisted_binomial(floor(m/d), floor(n/d))*moebius(d)

           for d in divisors(n+m+1))/(m+n+1)

CROSSREFS

Cf. A178738, A178749, A022553, A131868, A163210.

Sequence in context: A301572 A017868 A319573 * A017858 A167769 A119369

Adjacent sequences:  A178901 A178902 A178903 * A178905 A178906 A178907

KEYWORD

sign,tabl

AUTHOR

F. Chapoton, Jun 22 2010

EXTENSIONS

Terms a(82) onward added by G. C. Greubel, Dec 10 2017

STATUS

approved

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Last modified September 16 08:51 EDT 2019. Contains 327091 sequences. (Running on oeis4.)