A178904 - OEIS

A178904

This should be related to the Coxeter transformations of the posets of partitions in rectangular boxes of size m times n.

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

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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;

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-François Alcover, Feb 23 2017, adapted from Python *)

PROG

(Sage)

def twisted_binomial(m, n):

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

def coefficients_A(m, n):

return sum(twisted_binomial(m // d, n // d) * moebius(d)

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

matrix(ZZ, 8, 8, coefficients_A)

CROSSREFS

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

Sequence in context: A353158 A334476 A319573 * A017858 A167769 A119369

Adjacent sequences: A178901 A178902 A178903 * A178905 A178906 A178907