A059489 Expansion of generating function A_{UU}^(2)(4n;1,1,1).

1, 5, 66, 2431, 252586, 74327145, 62062015500, 147198472495020, 992340657705109416, 19023173201224270401428, 1037283901500845276138040124, 160915151663568862349180293275135, 71031251058324655345105192111798148156, 89229337105909072018801794323387547092631236

Offset: 0

Author

N. J. A. Sloane, Feb 04 2001

Keywords

• nonn
• easy

Links

• Paul Barry, Jacobsthal Decompositions of Pascal's Triangle, Ternary Trees, and Alternating Sign Matrices, Journal of Integer Sequences, 19, 2016, #16.3.5.
• G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv:math/0008184 [math.CO], 2000-2001. [Th. 5, but the formula is wrong]

Programs

Maple

A059489 := proc(n) local i, j, t1; t1 := (-3)^(n^2)*2^(2*n); for i to 2*n + 1 do for j to 2*n + 1 do if j mod 2 = 0 then t1 := t1*(3*j - 3*i + 2)/(j - i +2*n +1) end if end do end do; t1 end proc;