0,3

An alternating sign matrix is a matrix of 0's, 1's and -1's such that (a) the sum of each row and column is 1; (b) the nonzero entries in each row and column alternate in sign.

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 27 2009: (Start)

Starting with offset 1 = row sums of triangle A160708, and convolution square of A160707.

a(n) is odd iff n is a Jacobsthal number [Frey and Sellers, 2000].

Starting with offset 1 = row sums of triangle A160708.

Starting (1, 2, 7,...) = convolution square of A160707: [1, 1, 3, 18, 192,...]. (End)

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D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 (2005), 939-954.

Index entries for sequences related to factorial numbers

Index entries for "core" sequences

a(n) = Product_{k=0..n-1} (3k+1)!/(n+k)!.

The Hankel transform of A025748 is a(n)3^binomial(n,2).

a(n) = sqrt(A049503).

A005130 := proc(n) local k; mul((3*k+1)!/(n+k)!, k=0..n-1); end;

f[n_] := Product[(3k + 1)!/(n + k)!, {k, 0, n - 1}]; Table[ f[n], {n, 0, 17}] (from Robert G. Wilson v Jul 15 2004)

(PARI) a(n)=if(n<0, 0, prod(k=0, n-1, (3*k+1)!/(n+k)!))

(PARI) a(n)=local(A); if(n<0, 0, A=Vec((1-(1-9*x+O(x^(2*n)))^(1/3))/(3*x)); matdet(matrix(n, n, i, j, A[i+j-1]))/3^binomial(n, 2))

Cf. A006366, A048601, also A003827, A005156, A005158, A005160-A005164, A050204, A049503.

Cf. A160707, A160708.

Sequence in context: A066383 A011802 A007065 this_sequence A091669 A108042 A152559

Adjacent sequences: A005127 A005128 A005129 this_sequence A005131 A005132 A005133

nonn,easy,nice,core

N. J. A. Sloane (njas(AT)research.att.com).